Knots, Braids, and Mapping Class Groups--papers Dedicated to Joan S. Birman

Knots, Braids, and Mapping Class Groups--papers Dedicated to Joan S. Birman

Author: Jane Gilman

Publisher: American Mathematical Soc.

Published:

Total Pages: 202

ISBN-13: 9780821888278

DOWNLOAD EBOOK

There are a number of specialties in low-dimensional topology that can find in their ''family tree'' a common ancestry in the theory of surface mappings. These include knot theory as studied through the use of braid representations, and 3-manifolds as studied through the use of Heegaard splittings. The study of the surface mapping class group (the modular group) is of course a rich subject in its own right, with relations to many different fields of mathematics and theoreticalphysics. However, its most direct and remarkable manifestation is probably in the vast area of low-dimensional topology. Although the scene of this area has been changed dramatically and experienced significant expansion since the original publication of Professor Joan Birman's seminal work,Braids, Links,and Mapping Class Groups(Princeton University Press), she brought together mathematicians whose research span many specialties, all of common lineage. The topics covered are quite diverse. Yet they reflect well the aim and spirit of the conference: to explore how these various specialties in low-dimensional topology have diverged in the past 20-25 years, as well as to explore common threads and potential future directions of development. This volume is dedicated to Joan Birman by hercolleagues with deep admiration and appreciation of her contribution to low-dimensional topology.


Book Synopsis Knots, Braids, and Mapping Class Groups--papers Dedicated to Joan S. Birman by : Jane Gilman

Download or read book Knots, Braids, and Mapping Class Groups--papers Dedicated to Joan S. Birman written by Jane Gilman and published by American Mathematical Soc.. This book was released on with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are a number of specialties in low-dimensional topology that can find in their ''family tree'' a common ancestry in the theory of surface mappings. These include knot theory as studied through the use of braid representations, and 3-manifolds as studied through the use of Heegaard splittings. The study of the surface mapping class group (the modular group) is of course a rich subject in its own right, with relations to many different fields of mathematics and theoreticalphysics. However, its most direct and remarkable manifestation is probably in the vast area of low-dimensional topology. Although the scene of this area has been changed dramatically and experienced significant expansion since the original publication of Professor Joan Birman's seminal work,Braids, Links,and Mapping Class Groups(Princeton University Press), she brought together mathematicians whose research span many specialties, all of common lineage. The topics covered are quite diverse. Yet they reflect well the aim and spirit of the conference: to explore how these various specialties in low-dimensional topology have diverged in the past 20-25 years, as well as to explore common threads and potential future directions of development. This volume is dedicated to Joan Birman by hercolleagues with deep admiration and appreciation of her contribution to low-dimensional topology.

Knots, Braids, and Mapping Class Groups -- Papers Dedicated to Joan S. Birman

Knots, Braids, and Mapping Class Groups -- Papers Dedicated to Joan S. Birman

Author: Jane Gilman

Publisher: American Mathematical Soc.

Published: 2001

Total Pages: 200

ISBN-13: 0821829661

DOWNLOAD EBOOK

There are a number of specialties in low-dimensional topology that can find in their ``family tree'' a common ancestry in the theory of surface mappings. These include knot theory as studied through the use of braid representations, and 3-manifolds as studied through the use of Heegaard splittings. The study of the surface mapping class group (the modular group) is of course a rich subject in its own right, with relations to many different fields of mathematics and theoreticalphysics. However, its most direct and remarkable manifestation is probably in the vast area of low-dimensional topology. Although the scene of this area has been changed dramatically and experienced significant expansion since the original publication of Professor Joan Birman's seminal work,Braids, Links,and Mapping Class Groups(Princeton University Press), she brought together mathematicians whose research span many specialties, all of common lineage. The topics covered are quite diverse. Yet they reflect well the aim and spirit of the conference: to explore how these various specialties in low-dimensional topology have diverged in the past 20-25 years, as well as to explore common threads and potential future directions of development. This volume is dedicated to Joan Birman by hercolleagues with deep admiration and appreciation of her contribution to low-dimensional topology.


Book Synopsis Knots, Braids, and Mapping Class Groups -- Papers Dedicated to Joan S. Birman by : Jane Gilman

Download or read book Knots, Braids, and Mapping Class Groups -- Papers Dedicated to Joan S. Birman written by Jane Gilman and published by American Mathematical Soc.. This book was released on 2001 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are a number of specialties in low-dimensional topology that can find in their ``family tree'' a common ancestry in the theory of surface mappings. These include knot theory as studied through the use of braid representations, and 3-manifolds as studied through the use of Heegaard splittings. The study of the surface mapping class group (the modular group) is of course a rich subject in its own right, with relations to many different fields of mathematics and theoreticalphysics. However, its most direct and remarkable manifestation is probably in the vast area of low-dimensional topology. Although the scene of this area has been changed dramatically and experienced significant expansion since the original publication of Professor Joan Birman's seminal work,Braids, Links,and Mapping Class Groups(Princeton University Press), she brought together mathematicians whose research span many specialties, all of common lineage. The topics covered are quite diverse. Yet they reflect well the aim and spirit of the conference: to explore how these various specialties in low-dimensional topology have diverged in the past 20-25 years, as well as to explore common threads and potential future directions of development. This volume is dedicated to Joan Birman by hercolleagues with deep admiration and appreciation of her contribution to low-dimensional topology.

Braids, Links, and Mapping Class Groups

Braids, Links, and Mapping Class Groups

Author: Joan S. Birman

Publisher: Princeton University Press

Published: 1974

Total Pages: 244

ISBN-13: 9780691081496

DOWNLOAD EBOOK

The central theme of this study is Artin's braid group and the many ways that the notion of a braid has proved to be important in low-dimensional topology. In Chapter 1 the author is concerned with the concept of a braid as a group of motions of points in a manifold. She studies structural and algebraic properties of the braid groups of two manifolds, and derives systems of defining relations for the braid groups of the plane and sphere. In Chapter 2 she focuses on the connections between the classical braid group and the classical knot problem. After reviewing basic results she proceeds to an exploration of some possible implications of the Garside and Markov theorems. Chapter 3 offers discussion of matrix representations of the free group and of subgroups of the automorphism group of the free group. These ideas come to a focus in the difficult open question of whether Burau's matrix representation of the braid group is faithful. Chapter 4 is a broad view of recent results on the connections between braid groups and mapping class groups of surfaces. Chapter 5 contains a brief discussion of the theory of "plats." Research problems are included in an appendix.


Book Synopsis Braids, Links, and Mapping Class Groups by : Joan S. Birman

Download or read book Braids, Links, and Mapping Class Groups written by Joan S. Birman and published by Princeton University Press. This book was released on 1974 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central theme of this study is Artin's braid group and the many ways that the notion of a braid has proved to be important in low-dimensional topology. In Chapter 1 the author is concerned with the concept of a braid as a group of motions of points in a manifold. She studies structural and algebraic properties of the braid groups of two manifolds, and derives systems of defining relations for the braid groups of the plane and sphere. In Chapter 2 she focuses on the connections between the classical braid group and the classical knot problem. After reviewing basic results she proceeds to an exploration of some possible implications of the Garside and Markov theorems. Chapter 3 offers discussion of matrix representations of the free group and of subgroups of the automorphism group of the free group. These ideas come to a focus in the difficult open question of whether Burau's matrix representation of the braid group is faithful. Chapter 4 is a broad view of recent results on the connections between braid groups and mapping class groups of surfaces. Chapter 5 contains a brief discussion of the theory of "plats." Research problems are included in an appendix.

Braids, Links, and Mapping Class Groups. (AM-82), Volume 82

Braids, Links, and Mapping Class Groups. (AM-82), Volume 82

Author: Joan S. Birman

Publisher: Princeton University Press

Published: 2016-03-02

Total Pages: 237

ISBN-13: 1400881420

DOWNLOAD EBOOK

The central theme of this study is Artin's braid group and the many ways that the notion of a braid has proved to be important in low-dimensional topology. In Chapter 1 the author is concerned with the concept of a braid as a group of motions of points in a manifold. She studies structural and algebraic properties of the braid groups of two manifolds, and derives systems of defining relations for the braid groups of the plane and sphere. In Chapter 2 she focuses on the connections between the classical braid group and the classical knot problem. After reviewing basic results she proceeds to an exploration of some possible implications of the Garside and Markov theorems. Chapter 3 offers discussion of matrix representations of the free group and of subgroups of the automorphism group of the free group. These ideas come to a focus in the difficult open question of whether Burau's matrix representation of the braid group is faithful. Chapter 4 is a broad view of recent results on the connections between braid groups and mapping class groups of surfaces. Chapter 5 contains a brief discussion of the theory of "plats." Research problems are included in an appendix.


Book Synopsis Braids, Links, and Mapping Class Groups. (AM-82), Volume 82 by : Joan S. Birman

Download or read book Braids, Links, and Mapping Class Groups. (AM-82), Volume 82 written by Joan S. Birman and published by Princeton University Press. This book was released on 2016-03-02 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central theme of this study is Artin's braid group and the many ways that the notion of a braid has proved to be important in low-dimensional topology. In Chapter 1 the author is concerned with the concept of a braid as a group of motions of points in a manifold. She studies structural and algebraic properties of the braid groups of two manifolds, and derives systems of defining relations for the braid groups of the plane and sphere. In Chapter 2 she focuses on the connections between the classical braid group and the classical knot problem. After reviewing basic results she proceeds to an exploration of some possible implications of the Garside and Markov theorems. Chapter 3 offers discussion of matrix representations of the free group and of subgroups of the automorphism group of the free group. These ideas come to a focus in the difficult open question of whether Burau's matrix representation of the braid group is faithful. Chapter 4 is a broad view of recent results on the connections between braid groups and mapping class groups of surfaces. Chapter 5 contains a brief discussion of the theory of "plats." Research problems are included in an appendix.

Geometry and Topology of Submanifolds and Currents

Geometry and Topology of Submanifolds and Currents

Author: Weiping Li

Publisher: American Mathematical Soc.

Published: 2015-08-25

Total Pages: 200

ISBN-13: 1470415569

DOWNLOAD EBOOK

he papers in this volume are mainly from the 2013 Midwest Geometry Conference, held October 19, 2013, at Oklahoma State University, Stillwater, OK, and partly from the 2012 Midwest Geometry Conference, held May 12-13, 2012, at the University of Oklahoma, Norman, OK. The papers cover recent results on geometry and topology of submanifolds. On the topology side, topics include Plateau problems, Voevodsky's motivic cohomology, Reidemeister zeta function and systolic inequality, and freedom in 2- and 3-dimensional manifolds. On the geometry side, the authors discuss classifying isoparametric hypersurfaces and review Hartogs triangle, finite volume flows, nonexistence of stable p-currents, and a generalized Bernstein type problem. The authors also show that the interaction between topology and geometry is a key to deeply understanding topological invariants and the geometric problems.


Book Synopsis Geometry and Topology of Submanifolds and Currents by : Weiping Li

Download or read book Geometry and Topology of Submanifolds and Currents written by Weiping Li and published by American Mathematical Soc.. This book was released on 2015-08-25 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: he papers in this volume are mainly from the 2013 Midwest Geometry Conference, held October 19, 2013, at Oklahoma State University, Stillwater, OK, and partly from the 2012 Midwest Geometry Conference, held May 12-13, 2012, at the University of Oklahoma, Norman, OK. The papers cover recent results on geometry and topology of submanifolds. On the topology side, topics include Plateau problems, Voevodsky's motivic cohomology, Reidemeister zeta function and systolic inequality, and freedom in 2- and 3-dimensional manifolds. On the geometry side, the authors discuss classifying isoparametric hypersurfaces and review Hartogs triangle, finite volume flows, nonexistence of stable p-currents, and a generalized Bernstein type problem. The authors also show that the interaction between topology and geometry is a key to deeply understanding topological invariants and the geometric problems.

Zeta Functions of Graphs

Zeta Functions of Graphs

Author: Audrey Terras

Publisher: Cambridge University Press

Published: 2010-11-18

Total Pages: 253

ISBN-13: 1139491784

DOWNLOAD EBOOK

Graph theory meets number theory in this stimulating book. Ihara zeta functions of finite graphs are reciprocals of polynomials, sometimes in several variables. Analogies abound with number-theoretic functions such as Riemann/Dedekind zeta functions. For example, there is a Riemann hypothesis (which may be false) and prime number theorem for graphs. Explicit constructions of graph coverings use Galois theory to generalize Cayley and Schreier graphs. Then non-isomorphic simple graphs with the same zeta are produced, showing you cannot hear the shape of a graph. The spectra of matrices such as the adjacency and edge adjacency matrices of a graph are essential to the plot of this book, which makes connections with quantum chaos and random matrix theory, plus expander/Ramanujan graphs of interest in computer science. Created for beginning graduate students, the book will also appeal to researchers. Many well-chosen illustrations and exercises, both theoretical and computer-based, are included throughout.


Book Synopsis Zeta Functions of Graphs by : Audrey Terras

Download or read book Zeta Functions of Graphs written by Audrey Terras and published by Cambridge University Press. This book was released on 2010-11-18 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph theory meets number theory in this stimulating book. Ihara zeta functions of finite graphs are reciprocals of polynomials, sometimes in several variables. Analogies abound with number-theoretic functions such as Riemann/Dedekind zeta functions. For example, there is a Riemann hypothesis (which may be false) and prime number theorem for graphs. Explicit constructions of graph coverings use Galois theory to generalize Cayley and Schreier graphs. Then non-isomorphic simple graphs with the same zeta are produced, showing you cannot hear the shape of a graph. The spectra of matrices such as the adjacency and edge adjacency matrices of a graph are essential to the plot of this book, which makes connections with quantum chaos and random matrix theory, plus expander/Ramanujan graphs of interest in computer science. Created for beginning graduate students, the book will also appeal to researchers. Many well-chosen illustrations and exercises, both theoretical and computer-based, are included throughout.

Lectures in Knot Theory

Lectures in Knot Theory

Author: Józef H. Przytycki

Publisher: Springer Nature

Published:

Total Pages: 525

ISBN-13: 3031400445

DOWNLOAD EBOOK


Book Synopsis Lectures in Knot Theory by : Józef H. Przytycki

Download or read book Lectures in Knot Theory written by Józef H. Przytycki and published by Springer Nature. This book was released on with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Applications of Knot Theory

Applications of Knot Theory

Author: American Mathematical Society. Short Course

Publisher: American Mathematical Soc.

Published: 2009

Total Pages: 203

ISBN-13: 0821844660

DOWNLOAD EBOOK

Louis Kauffman discusses applications of knot theory to physics, Nadrian Seeman discusses how topology is used in DNA nanotechnology, and Jonathan Simon discusses the statistical and energetic properties of knots and their relation to molecular biology."--BOOK JACKET.


Book Synopsis Applications of Knot Theory by : American Mathematical Society. Short Course

Download or read book Applications of Knot Theory written by American Mathematical Society. Short Course and published by American Mathematical Soc.. This book was released on 2009 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: Louis Kauffman discusses applications of knot theory to physics, Nadrian Seeman discusses how topology is used in DNA nanotechnology, and Jonathan Simon discusses the statistical and energetic properties of knots and their relation to molecular biology."--BOOK JACKET.

Sets And Computations

Sets And Computations

Author: Sy-david Friedman

Publisher: World Scientific

Published: 2017-06-22

Total Pages: 280

ISBN-13: 9813223537

DOWNLOAD EBOOK

The contents in this volume are based on the program Sets and Computations that was held at the Institute for Mathematical Sciences, National University of Singapore from 30 March until 30 April 2015. This special collection reports on important and recent interactions between the fields of Set Theory and Computation Theory. This includes the new research areas of computational complexity in set theory, randomness beyond the hyperarithmetic, powerful extensions of Goodstein's theorem and the capturing of large fragments of set theory via elementary-recursive structures.Further chapters are concerned with central topics within Set Theory, including cardinal characteristics, Fraïssé limits, the set-generic multiverse and the study of ideals. Also Computation Theory, which includes computable group theory and measure-theoretic aspects of Hilbert's Tenth Problem. A volume of this broad scope will appeal to a wide spectrum of researchers in mathematical logic.


Book Synopsis Sets And Computations by : Sy-david Friedman

Download or read book Sets And Computations written by Sy-david Friedman and published by World Scientific. This book was released on 2017-06-22 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contents in this volume are based on the program Sets and Computations that was held at the Institute for Mathematical Sciences, National University of Singapore from 30 March until 30 April 2015. This special collection reports on important and recent interactions between the fields of Set Theory and Computation Theory. This includes the new research areas of computational complexity in set theory, randomness beyond the hyperarithmetic, powerful extensions of Goodstein's theorem and the capturing of large fragments of set theory via elementary-recursive structures.Further chapters are concerned with central topics within Set Theory, including cardinal characteristics, Fraïssé limits, the set-generic multiverse and the study of ideals. Also Computation Theory, which includes computable group theory and measure-theoretic aspects of Hilbert's Tenth Problem. A volume of this broad scope will appeal to a wide spectrum of researchers in mathematical logic.

Topology and Physics

Topology and Physics

Author: Kevin Lin

Publisher: World Scientific

Published: 2008

Total Pages: 466

ISBN-13: 981281910X

DOWNLOAD EBOOK

This unique volume, resulting from a conference at the Chern Institute of Mathematics dedicated to the memory of Xiao-Song Lin, presents a broad connection between topology and physics as exemplified by the relationship between low-dimensional topology and quantum field theory.The volume includes works on picture (2+1)-TQFTs and their applications to quantum computing, Berry phase and Yang?Baxterization of the braid relation, finite type invariant of knots, categorification and Khovanov homology, Gromov?Witten type invariants, twisted Alexander polynomials, Faddeev knots, generalized Ricci flow, Calabi?Yau problems for CR manifolds, Milnor's conjecture on volume of simplexes, Heegaard genera of 3-manifolds, and the (A,B)-slice problem. It also includes five unpublished papers of Xiao-Song Lin and various speeches related to the memorial conference.


Book Synopsis Topology and Physics by : Kevin Lin

Download or read book Topology and Physics written by Kevin Lin and published by World Scientific. This book was released on 2008 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique volume, resulting from a conference at the Chern Institute of Mathematics dedicated to the memory of Xiao-Song Lin, presents a broad connection between topology and physics as exemplified by the relationship between low-dimensional topology and quantum field theory.The volume includes works on picture (2+1)-TQFTs and their applications to quantum computing, Berry phase and Yang?Baxterization of the braid relation, finite type invariant of knots, categorification and Khovanov homology, Gromov?Witten type invariants, twisted Alexander polynomials, Faddeev knots, generalized Ricci flow, Calabi?Yau problems for CR manifolds, Milnor's conjecture on volume of simplexes, Heegaard genera of 3-manifolds, and the (A,B)-slice problem. It also includes five unpublished papers of Xiao-Song Lin and various speeches related to the memorial conference.