Pseudo-periodic Maps and Degeneration of Riemann Surfaces

Pseudo-periodic Maps and Degeneration of Riemann Surfaces

Author: Yukio Matsumoto

Publisher: Springer

Published: 2011-08-17

Total Pages: 251

ISBN-13: 3642225349

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The first part of the book studies pseudo-periodic maps of a closed surface of genus greater than or equal to two. This class of homeomorphisms was originally introduced by J. Nielsen in 1944 as an extension of periodic maps. In this book, the conjugacy classes of the (chiral) pseudo-periodic mapping classes are completely classified, and Nielsen's incomplete classification is corrected. The second part applies the results of the first part to the topology of degeneration of Riemann surfaces. It is shown that the set of topological types of all the singular fibers appearing in one parameter holomorphic families of Riemann surfaces is in a bijective correspondence with the set of conjugacy classes of the pseudo-periodic maps of negative twists. The correspondence is given by the topological monodromy.


Book Synopsis Pseudo-periodic Maps and Degeneration of Riemann Surfaces by : Yukio Matsumoto

Download or read book Pseudo-periodic Maps and Degeneration of Riemann Surfaces written by Yukio Matsumoto and published by Springer. This book was released on 2011-08-17 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first part of the book studies pseudo-periodic maps of a closed surface of genus greater than or equal to two. This class of homeomorphisms was originally introduced by J. Nielsen in 1944 as an extension of periodic maps. In this book, the conjugacy classes of the (chiral) pseudo-periodic mapping classes are completely classified, and Nielsen's incomplete classification is corrected. The second part applies the results of the first part to the topology of degeneration of Riemann surfaces. It is shown that the set of topological types of all the singular fibers appearing in one parameter holomorphic families of Riemann surfaces is in a bijective correspondence with the set of conjugacy classes of the pseudo-periodic maps of negative twists. The correspondence is given by the topological monodromy.

Pseudo-periodic Maps and Degeneration of Riemann Surfaces

Pseudo-periodic Maps and Degeneration of Riemann Surfaces

Author: Yukio Matsumoto

Publisher: Springer

Published: 2011-08-20

Total Pages: 240

ISBN-13: 9783642225352

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The first part of the book studies pseudo-periodic maps of a closed surface of genus greater than or equal to two. This class of homeomorphisms was originally introduced by J. Nielsen in 1944 as an extension of periodic maps. In this book, the conjugacy classes of the (chiral) pseudo-periodic mapping classes are completely classified, and Nielsen's incomplete classification is corrected. The second part applies the results of the first part to the topology of degeneration of Riemann surfaces. It is shown that the set of topological types of all the singular fibers appearing in one parameter holomorphic families of Riemann surfaces is in a bijective correspondence with the set of conjugacy classes of the pseudo-periodic maps of negative twists. The correspondence is given by the topological monodromy.


Book Synopsis Pseudo-periodic Maps and Degeneration of Riemann Surfaces by : Yukio Matsumoto

Download or read book Pseudo-periodic Maps and Degeneration of Riemann Surfaces written by Yukio Matsumoto and published by Springer. This book was released on 2011-08-20 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first part of the book studies pseudo-periodic maps of a closed surface of genus greater than or equal to two. This class of homeomorphisms was originally introduced by J. Nielsen in 1944 as an extension of periodic maps. In this book, the conjugacy classes of the (chiral) pseudo-periodic mapping classes are completely classified, and Nielsen's incomplete classification is corrected. The second part applies the results of the first part to the topology of degeneration of Riemann surfaces. It is shown that the set of topological types of all the singular fibers appearing in one parameter holomorphic families of Riemann surfaces is in a bijective correspondence with the set of conjugacy classes of the pseudo-periodic maps of negative twists. The correspondence is given by the topological monodromy.

Singularities in Geometry and Topology

Singularities in Geometry and Topology

Author: Jean-Paul Brasselet

Publisher: World Scientific

Published: 2007

Total Pages: 918

ISBN-13: 981270681X

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Singularity theory appears in numerous branches of mathematics, as well as in many emerging areas such as robotics, control theory, imaging, and various evolving areas in physics. The purpose of this proceedings volume is to cover recent developments in singularity theory and to introduce young researchers from developing countries to singularities in geometry and topology. The contributions discuss singularities in both complex and real geometry. As such, they provide a natural continuation of the previous school on singularities held at ICTP (1991), which is recognized as having had a major influence in the field.


Book Synopsis Singularities in Geometry and Topology by : Jean-Paul Brasselet

Download or read book Singularities in Geometry and Topology written by Jean-Paul Brasselet and published by World Scientific. This book was released on 2007 with total page 918 pages. Available in PDF, EPUB and Kindle. Book excerpt: Singularity theory appears in numerous branches of mathematics, as well as in many emerging areas such as robotics, control theory, imaging, and various evolving areas in physics. The purpose of this proceedings volume is to cover recent developments in singularity theory and to introduce young researchers from developing countries to singularities in geometry and topology. The contributions discuss singularities in both complex and real geometry. As such, they provide a natural continuation of the previous school on singularities held at ICTP (1991), which is recognized as having had a major influence in the field.

Singularities In Geometry And Topology - Proceedings Of The Trieste Singularity Summer School And Workshop

Singularities In Geometry And Topology - Proceedings Of The Trieste Singularity Summer School And Workshop

Author: Jean-paul Brasselet

Publisher: World Scientific

Published: 2007-01-16

Total Pages: 917

ISBN-13: 9814477044

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Singularity theory appears in numerous branches of mathematics, as well as in many emerging areas such as robotics, control theory, imaging, and various evolving areas in physics. The purpose of this proceedings volume is to cover recent developments in singularity theory and to introduce young researchers from developing countries to singularities in geometry and topology.The contributions discuss singularities in both complex and real geometry. As such, they provide a natural continuation of the previous school on singularities held at ICTP (1991), which is recognized as having had a major influence in the field.


Book Synopsis Singularities In Geometry And Topology - Proceedings Of The Trieste Singularity Summer School And Workshop by : Jean-paul Brasselet

Download or read book Singularities In Geometry And Topology - Proceedings Of The Trieste Singularity Summer School And Workshop written by Jean-paul Brasselet and published by World Scientific. This book was released on 2007-01-16 with total page 917 pages. Available in PDF, EPUB and Kindle. Book excerpt: Singularity theory appears in numerous branches of mathematics, as well as in many emerging areas such as robotics, control theory, imaging, and various evolving areas in physics. The purpose of this proceedings volume is to cover recent developments in singularity theory and to introduce young researchers from developing countries to singularities in geometry and topology.The contributions discuss singularities in both complex and real geometry. As such, they provide a natural continuation of the previous school on singularities held at ICTP (1991), which is recognized as having had a major influence in the field.

Splitting Deformations of Degenerations of Complex Curves

Splitting Deformations of Degenerations of Complex Curves

Author: Shigeru Takamura

Publisher: Springer

Published: 2006-10-11

Total Pages: 583

ISBN-13: 3540333649

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Here is a deformation theory for degenerations of complex curves; specifically, discussing deformations which induce splitting of the singular fiber of a degeneration. The author constructs a deformation of the degeneration in such a way that a subdivisor is "barked," or peeled off from the singular fiber. "Barking deformations" are related to deformations of surface singularities, in particular, cyclic quotient singularities, as well as the mapping class groups of Riemann surfaces via monodromies.


Book Synopsis Splitting Deformations of Degenerations of Complex Curves by : Shigeru Takamura

Download or read book Splitting Deformations of Degenerations of Complex Curves written by Shigeru Takamura and published by Springer. This book was released on 2006-10-11 with total page 583 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here is a deformation theory for degenerations of complex curves; specifically, discussing deformations which induce splitting of the singular fiber of a degeneration. The author constructs a deformation of the degeneration in such a way that a subdivisor is "barked," or peeled off from the singular fiber. "Barking deformations" are related to deformations of surface singularities, in particular, cyclic quotient singularities, as well as the mapping class groups of Riemann surfaces via monodromies.

Geometric topology

Geometric topology

Author: William Hilal Kazez

Publisher: American Mathematical Soc.

Published: 1997

Total Pages: 500

ISBN-13: 9780821806531

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Covers the proceedings of the 1993 Georgia International Topology Conference held at the University of Georgia during the month of August. This work includes Kirby's problem list, which contains a description of the progress made on each of the problems and includes a bibliography. It is suitable for those interested in the many areas of topology.


Book Synopsis Geometric topology by : William Hilal Kazez

Download or read book Geometric topology written by William Hilal Kazez and published by American Mathematical Soc.. This book was released on 1997 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers the proceedings of the 1993 Georgia International Topology Conference held at the University of Georgia during the month of August. This work includes Kirby's problem list, which contains a description of the progress made on each of the problems and includes a bibliography. It is suitable for those interested in the many areas of topology.

Introduction to Lipschitz Geometry of Singularities

Introduction to Lipschitz Geometry of Singularities

Author: Walter Neumann

Publisher: Springer Nature

Published: 2021-01-11

Total Pages: 356

ISBN-13: 3030618072

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This book presents a broad overview of the important recent progress which led to the emergence of new ideas in Lipschitz geometry and singularities, and started to build bridges to several major areas of singularity theory. Providing all the necessary background in a series of introductory lectures, it also contains Pham and Teissier's previously unpublished pioneering work on the Lipschitz classification of germs of plane complex algebraic curves. While a real or complex algebraic variety is topologically locally conical, it is in general not metrically conical; there are parts of its link with non-trivial topology which shrink faster than linearly when approaching the special point. The essence of the Lipschitz geometry of singularities is captured by the problem of building classifications of the germs up to local bi-Lipschitz homeomorphism. The Lipschitz geometry of a singular space germ is then its equivalence class in this category. The book is aimed at graduate students and researchers from other fields of geometry who are interested in studying the multiple open questions offered by this new subject.


Book Synopsis Introduction to Lipschitz Geometry of Singularities by : Walter Neumann

Download or read book Introduction to Lipschitz Geometry of Singularities written by Walter Neumann and published by Springer Nature. This book was released on 2021-01-11 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a broad overview of the important recent progress which led to the emergence of new ideas in Lipschitz geometry and singularities, and started to build bridges to several major areas of singularity theory. Providing all the necessary background in a series of introductory lectures, it also contains Pham and Teissier's previously unpublished pioneering work on the Lipschitz classification of germs of plane complex algebraic curves. While a real or complex algebraic variety is topologically locally conical, it is in general not metrically conical; there are parts of its link with non-trivial topology which shrink faster than linearly when approaching the special point. The essence of the Lipschitz geometry of singularities is captured by the problem of building classifications of the germs up to local bi-Lipschitz homeomorphism. The Lipschitz geometry of a singular space germ is then its equivalence class in this category. The book is aimed at graduate students and researchers from other fields of geometry who are interested in studying the multiple open questions offered by this new subject.

Handbook of Teichmüller Theory

Handbook of Teichmüller Theory

Author: Athanase Papadopoulos

Publisher: European Mathematical Society

Published: 2007

Total Pages: 888

ISBN-13: 9783037190555

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This multi-volume set deals with Teichmuller theory in the broadest sense, namely, as the study of moduli space of geometric structures on surfaces, with methods inspired or adapted from those of classical Teichmuller theory. The aim is to give a complete panorama of this generalized Teichmuller theory and of its applications in various fields of mathematics. The volumes consist of chapters, each of which is dedicated to a specific topic. The volume has 19 chapters and is divided into four parts: The metric and the analytic theory (uniformization, Weil-Petersson geometry, holomorphic families of Riemann surfaces, infinite-dimensional Teichmuller spaces, cohomology of moduli space, and the intersection theory of moduli space). The group theory (quasi-homomorphisms of mapping class groups, measurable rigidity of mapping class groups, applications to Lefschetz fibrations, affine groups of flat surfaces, braid groups, and Artin groups). Representation spaces and geometric structures (trace coordinates, invariant theory, complex projective structures, circle packings, and moduli spaces of Lorentz manifolds homeomorphic to the product of a surface with the real line). The Grothendieck-Teichmuller theory (dessins d'enfants, Grothendieck's reconstruction principle, and the Teichmuller theory of the solenoid). This handbook is an essential reference for graduate students and researchers interested in Teichmuller theory and its ramifications, in particular for mathematicians working in topology, geometry, algebraic geometry, dynamical systems and complex analysis. The authors are leading experts in the field.


Book Synopsis Handbook of Teichmüller Theory by : Athanase Papadopoulos

Download or read book Handbook of Teichmüller Theory written by Athanase Papadopoulos and published by European Mathematical Society. This book was released on 2007 with total page 888 pages. Available in PDF, EPUB and Kindle. Book excerpt: This multi-volume set deals with Teichmuller theory in the broadest sense, namely, as the study of moduli space of geometric structures on surfaces, with methods inspired or adapted from those of classical Teichmuller theory. The aim is to give a complete panorama of this generalized Teichmuller theory and of its applications in various fields of mathematics. The volumes consist of chapters, each of which is dedicated to a specific topic. The volume has 19 chapters and is divided into four parts: The metric and the analytic theory (uniformization, Weil-Petersson geometry, holomorphic families of Riemann surfaces, infinite-dimensional Teichmuller spaces, cohomology of moduli space, and the intersection theory of moduli space). The group theory (quasi-homomorphisms of mapping class groups, measurable rigidity of mapping class groups, applications to Lefschetz fibrations, affine groups of flat surfaces, braid groups, and Artin groups). Representation spaces and geometric structures (trace coordinates, invariant theory, complex projective structures, circle packings, and moduli spaces of Lorentz manifolds homeomorphic to the product of a surface with the real line). The Grothendieck-Teichmuller theory (dessins d'enfants, Grothendieck's reconstruction principle, and the Teichmuller theory of the solenoid). This handbook is an essential reference for graduate students and researchers interested in Teichmuller theory and its ramifications, in particular for mathematicians working in topology, geometry, algebraic geometry, dynamical systems and complex analysis. The authors are leading experts in the field.

Conformal Mapping on Riemann Surfaces

Conformal Mapping on Riemann Surfaces

Author: Harvey Cohn

Publisher: Courier Corporation

Published: 2014-05-05

Total Pages: 352

ISBN-13: 0486153290

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Lucid, insightful exploration reviews complex analysis, introduces Riemann manifold, shows how to define real functions on manifolds, and more. Perfect for classroom use or independent study. 344 exercises. 1967 edition.


Book Synopsis Conformal Mapping on Riemann Surfaces by : Harvey Cohn

Download or read book Conformal Mapping on Riemann Surfaces written by Harvey Cohn and published by Courier Corporation. This book was released on 2014-05-05 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lucid, insightful exploration reviews complex analysis, introduces Riemann manifold, shows how to define real functions on manifolds, and more. Perfect for classroom use or independent study. 344 exercises. 1967 edition.

Mathematical Reviews

Mathematical Reviews

Author:

Publisher:

Published: 2008

Total Pages: 916

ISBN-13:

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Book Synopsis Mathematical Reviews by :

Download or read book Mathematical Reviews written by and published by . This book was released on 2008 with total page 916 pages. Available in PDF, EPUB and Kindle. Book excerpt: