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Presents discussion of formal groups and an introduction to BP-homology. This book features a section on unstable operations. It is suitable for graduate students and algebraic topologists.
Book Synopsis Brown-Peterson Homology: An Introduction and Sampler by : W. Stephen Wilson
Download or read book Brown-Peterson Homology: An Introduction and Sampler written by W. Stephen Wilson and published by American Mathematical Soc.. This book was released on 1982-12-31 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents discussion of formal groups and an introduction to BP-homology. This book features a section on unstable operations. It is suitable for graduate students and algebraic topologists.
Since the publication of its first edition, this book has served as one of the few available on the classical Adams spectral sequence, and is the best account on the Adams-Novikov spectral sequence. This new edition has been updated in many places, especially the final chapter, which has been completely rewritten with an eye toward future research in the field. It remains the definitive reference on the stable homotopy groups of spheres. The first three chapters introduce the homotopy groups of spheres and take the reader from the classical results in the field though the computational aspects of the classical Adams spectral sequence and its modifications, which are the main tools topologists have to investigate the homotopy groups of spheres. Nowadays, the most efficient tools are the Brown-Peterson theory, the Adams-Novikov spectral sequence, and the chromatic spectral sequence, a device for analyzing the global structure of the stable homotopy groups of spheres and relating them to the cohomology of the Morava stabilizer groups. These topics are described in detail in Chapters 4 to 6. The revamped Chapter 7 is the computational payoff of the book, yielding a lot of information about the stable homotopy group of spheres. Appendices follow, giving self-contained accounts of the theory of formal group laws and the homological algebra associated with Hopf algebras and Hopf algebroids. The book is intended for anyone wishing to study computational stable homotopy theory. It is accessible to graduate students with a knowledge of algebraic topology and recommended to anyone wishing to venture into the frontiers of the subject.
Book Synopsis Complex Cobordism and Stable Homotopy Groups of Spheres by : Douglas C. Ravenel
Download or read book Complex Cobordism and Stable Homotopy Groups of Spheres written by Douglas C. Ravenel and published by American Mathematical Society. This book was released on 2023-02-09 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the publication of its first edition, this book has served as one of the few available on the classical Adams spectral sequence, and is the best account on the Adams-Novikov spectral sequence. This new edition has been updated in many places, especially the final chapter, which has been completely rewritten with an eye toward future research in the field. It remains the definitive reference on the stable homotopy groups of spheres. The first three chapters introduce the homotopy groups of spheres and take the reader from the classical results in the field though the computational aspects of the classical Adams spectral sequence and its modifications, which are the main tools topologists have to investigate the homotopy groups of spheres. Nowadays, the most efficient tools are the Brown-Peterson theory, the Adams-Novikov spectral sequence, and the chromatic spectral sequence, a device for analyzing the global structure of the stable homotopy groups of spheres and relating them to the cohomology of the Morava stabilizer groups. These topics are described in detail in Chapters 4 to 6. The revamped Chapter 7 is the computational payoff of the book, yielding a lot of information about the stable homotopy group of spheres. Appendices follow, giving self-contained accounts of the theory of formal group laws and the homological algebra associated with Hopf algebras and Hopf algebroids. The book is intended for anyone wishing to study computational stable homotopy theory. It is accessible to graduate students with a knowledge of algebraic topology and recommended to anyone wishing to venture into the frontiers of the subject.
Book Synopsis Canadian Journal of Mathematics by :
Download or read book Canadian Journal of Mathematics written by and published by . This book was released on 1994 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to Some Methods of Algebraic $K$-Theory by : Hyman Bass
Download or read book Introduction to Some Methods of Algebraic $K$-Theory written by Hyman Bass and published by American Mathematical Soc.. This book was released on 1974-12-31 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Introduces some of the main ideas of modern intersection theory, traces their origins in classical geometry and sketches a few typical applications. Suitable for graduate students in mathematics, this book describes the construction and computation of intersection products by means of the geometry of normal cones.
Book Synopsis Introduction to Intersection Theory in Algebraic Geometry by : William Fulton
Download or read book Introduction to Intersection Theory in Algebraic Geometry written by William Fulton and published by American Mathematical Soc.. This book was released on 1984 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduces some of the main ideas of modern intersection theory, traces their origins in classical geometry and sketches a few typical applications. Suitable for graduate students in mathematics, this book describes the construction and computation of intersection products by means of the geometry of normal cones.
Delivers a broad, conceptual introduction to chromatic homotopy theory, focusing on contact with arithmetic and algebraic geometry.
Book Synopsis Formal Geometry and Bordism Operations by : Eric Peterson
Download or read book Formal Geometry and Bordism Operations written by Eric Peterson and published by Cambridge University Press. This book was released on 2019 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: Delivers a broad, conceptual introduction to chromatic homotopy theory, focusing on contact with arithmetic and algebraic geometry.
As part of the scientific activity in connection with the 70th birthday of the Adam Mickiewicz University in Poznan, an international conference on algebraic topology was held. In the resulting proceedings volume, the emphasis is on substantial survey papers, some presented at the conference, some written subsequently.
Book Synopsis Algebraic Topology. Poznan 1989 by : Stefan Jackowski
Download or read book Algebraic Topology. Poznan 1989 written by Stefan Jackowski and published by Springer. This book was released on 2006-11-14 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: As part of the scientific activity in connection with the 70th birthday of the Adam Mickiewicz University in Poznan, an international conference on algebraic topology was held. In the resulting proceedings volume, the emphasis is on substantial survey papers, some presented at the conference, some written subsequently.
This volume focuses on discussing the interplay between the analysis, as exemplified by the eta invariant and other spectral invariants, the number theory, as exemplified by the relevant Dedekind sums and Rademacher reciprocity, the algebraic topology, as exemplified by the equivariant bordism groups, K-theory groups, and connective K-theory groups, and the geometry of spherical space forms, as exemplified by the Smith homomorphism. These are used to study the existence of metrics of positive scalar curvature on spin manifolds of dimension at least 5 whose fundamental group is a spherical space form group. This volume is a completely rewritten revision of the first edition. The underlying organization is modified to provide a better organized and more coherent treatment of the material involved. In addition, approximately 100 pages have been added to study the existence of metrics of positive scalar curvature on spin manifolds of dimension at least 5 whose fundamental group is a spherical space form group. We have chosen to focus on the geometric aspect of the theory rather than more abstract algebraic constructions (like the assembly map) and to restrict our attention to spherical space forms rather than more general and more complicated geometrical examples to avoid losing contact with the fundamental geometry which is involved. Contents: Partial Differential OperatorsK Theory and CohomologyEquivariant BordismPositive Scalar CurvatureAuxiliary Materials Readership: Graduate students and researchers interested in global analysis, geometry, and topology. Keywords: Dedekind Sums and Rademacher Reciprocity;K-Theory;Eta Invariant;Spherical Space Form;Lens Space;Quaternion Spherical Space Form;Iterated Jet Bundle;Equivariant Bordism;Smith Homomorphism;Connective K-Theory;Manifolds with Positive Scalar Curvature;Spin Bordism;Unitary Bordism;Spin-C Bordism;Pin-C BordismReview: Key Features: The is a complete revision of the first edition and includes substantial amounts of new material applying the basic material of the book to the examination of metrics of positive scalar curvature on spin manifolds of dimension at least 5 whose fundamental group is a spherical space form groupTo ensure that the book is accessible to wide an audience as possible, there is a review of vector bundle theory, of Clifford module theory, of the Atiyah–Singer index theorem, and of the index theorem with boundaryThere are also tables, which have been simplified and the organization improved from the first edition, giving various K-theory and equivariant bordism groups
Book Synopsis Geometry Of Spherical Space Form Groups, The (Second Edition) by : Gilkey Peter B
Download or read book Geometry Of Spherical Space Form Groups, The (Second Edition) written by Gilkey Peter B and published by World Scientific. This book was released on 2018-01-03 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume focuses on discussing the interplay between the analysis, as exemplified by the eta invariant and other spectral invariants, the number theory, as exemplified by the relevant Dedekind sums and Rademacher reciprocity, the algebraic topology, as exemplified by the equivariant bordism groups, K-theory groups, and connective K-theory groups, and the geometry of spherical space forms, as exemplified by the Smith homomorphism. These are used to study the existence of metrics of positive scalar curvature on spin manifolds of dimension at least 5 whose fundamental group is a spherical space form group. This volume is a completely rewritten revision of the first edition. The underlying organization is modified to provide a better organized and more coherent treatment of the material involved. In addition, approximately 100 pages have been added to study the existence of metrics of positive scalar curvature on spin manifolds of dimension at least 5 whose fundamental group is a spherical space form group. We have chosen to focus on the geometric aspect of the theory rather than more abstract algebraic constructions (like the assembly map) and to restrict our attention to spherical space forms rather than more general and more complicated geometrical examples to avoid losing contact with the fundamental geometry which is involved. Contents: Partial Differential OperatorsK Theory and CohomologyEquivariant BordismPositive Scalar CurvatureAuxiliary Materials Readership: Graduate students and researchers interested in global analysis, geometry, and topology. Keywords: Dedekind Sums and Rademacher Reciprocity;K-Theory;Eta Invariant;Spherical Space Form;Lens Space;Quaternion Spherical Space Form;Iterated Jet Bundle;Equivariant Bordism;Smith Homomorphism;Connective K-Theory;Manifolds with Positive Scalar Curvature;Spin Bordism;Unitary Bordism;Spin-C Bordism;Pin-C BordismReview: Key Features: The is a complete revision of the first edition and includes substantial amounts of new material applying the basic material of the book to the examination of metrics of positive scalar curvature on spin manifolds of dimension at least 5 whose fundamental group is a spherical space form groupTo ensure that the book is accessible to wide an audience as possible, there is a review of vector bundle theory, of Clifford module theory, of the Atiyah–Singer index theorem, and of the index theorem with boundaryThere are also tables, which have been simplified and the organization improved from the first edition, giving various K-theory and equivariant bordism groups
This volume presents the proceedings from the month-long program held at Johns Hopkins University (Baltimore, MD) on homotopy theory, sponsored by the Japan-U.S. Mathematics Institute (JAMI). The book begins with historical accounts on the work of Professors Peter Landweber and Stewart Priddy. Central among the other topics are the following: 1. classical and nonclassical theory of $H$-spaces, compact groups, and finite groups, 2. classical and chromatic homotopy theory andlocalization, 3. classical and topological Hochschild cohomology, 4. elliptic cohomology and its relation to Moonshine and topological modular forms, and 5. motivic cohomology and Chow rings. This volume surveys the current state of research in these areas and offers an overview of futuredirections.
Book Synopsis Recent Progress in Homotopy Theory by : Donald M. Davis
Download or read book Recent Progress in Homotopy Theory written by Donald M. Davis and published by American Mathematical Soc.. This book was released on 2002 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the proceedings from the month-long program held at Johns Hopkins University (Baltimore, MD) on homotopy theory, sponsored by the Japan-U.S. Mathematics Institute (JAMI). The book begins with historical accounts on the work of Professors Peter Landweber and Stewart Priddy. Central among the other topics are the following: 1. classical and nonclassical theory of $H$-spaces, compact groups, and finite groups, 2. classical and chromatic homotopy theory andlocalization, 3. classical and topological Hochschild cohomology, 4. elliptic cohomology and its relation to Moonshine and topological modular forms, and 5. motivic cohomology and Chow rings. This volume surveys the current state of research in these areas and offers an overview of futuredirections.
In this volume, the geometry of spherical space form groups is studied using the eta invariant. The author reviews the analytical properties of the eta invariant of Atiyah-Patodi-Singer and describes how the eta invariant gives rise to torsion invariants in both K-theory and equivariant bordism. The eta invariant is used to compute the K-theory of spherical space forms, and to study the equivariant unitary bordism of spherical space forms and the Pinc and Spinc equivariant bordism groups for spherical space form groups. This leads to a complete structure theorem for these bordism and K-theory groups.There is a deep relationship between topology and analysis with differential geometry serving as the bridge. This book is intended to serve as an introduction to this subject for people from different research backgrounds.This book is intended as a research monograph for people who are not experts in all the areas discussed. It is written for topologists wishing to understand some of the analytic details and for analysists wishing to understand some of the topological ideas. It is also intended as an introduction to the field for graduate students.
Book Synopsis The Geometry of Spherical Space Form Groups by : Peter B. Gilkey
Download or read book The Geometry of Spherical Space Form Groups written by Peter B. Gilkey and published by World Scientific. This book was released on 1989 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, the geometry of spherical space form groups is studied using the eta invariant. The author reviews the analytical properties of the eta invariant of Atiyah-Patodi-Singer and describes how the eta invariant gives rise to torsion invariants in both K-theory and equivariant bordism. The eta invariant is used to compute the K-theory of spherical space forms, and to study the equivariant unitary bordism of spherical space forms and the Pinc and Spinc equivariant bordism groups for spherical space form groups. This leads to a complete structure theorem for these bordism and K-theory groups.There is a deep relationship between topology and analysis with differential geometry serving as the bridge. This book is intended to serve as an introduction to this subject for people from different research backgrounds.This book is intended as a research monograph for people who are not experts in all the areas discussed. It is written for topologists wishing to understand some of the analytic details and for analysists wishing to understand some of the topological ideas. It is also intended as an introduction to the field for graduate students.
