Complex Cobordism And Stable Homotopy Groups Of Spheres
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Complex Cobordism And Stable Homotopy Groups Of Spheres
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Author : Douglas C. Ravenel
language : en
Publisher: American Mathematical Soc.
Release Date : 2003-11-25
Complex Cobordism And Stable Homotopy Groups Of Spheres written by Douglas C. Ravenel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-11-25 with Mathematics categories.
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.
Complex Cobordism And Stable Homotopy Groups Of Spheres
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Author : Douglas C. Ravenel
language : en
Publisher: American Mathematical Society
Release Date : 2023-02-09
Complex Cobordism And Stable Homotopy Groups Of Spheres written by Douglas C. Ravenel and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-09 with Mathematics categories.
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.
Stable Homotopy Groups Of Spheres
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Author : Stanley O. Kochman
language : en
Publisher: Springer
Release Date : 2006-11-14
Stable Homotopy Groups Of Spheres written by Stanley O. Kochman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
A central problem in algebraic topology is the calculation of the values of the stable homotopy groups of spheres +*S. In this book, a new method for this is developed based upon the analysis of the Atiyah-Hirzebruch spectral sequence. After the tools for this analysis are developed, these methods are applied to compute inductively the first 64 stable stems, a substantial improvement over the previously known 45. Much of this computation is algorithmic and is done by computer. As an application, an element of degree 62 of Kervaire invariant one is shown to have order two. This book will be useful to algebraic topologists and graduate students with a knowledge of basic homotopy theory and Brown-Peterson homology; for its methods, as a reference on the structure of the first 64 stable stems and for the tables depicting the behavior of the Atiyah-Hirzebruch and classical Adams spectral sequences through degree 64.
Stable Stems
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Author : Daniel C. Isaksen
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-02-13
Stable Stems written by Daniel C. Isaksen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-13 with Education categories.
The author presents a detailed analysis of 2-complete stable homotopy groups, both in the classical context and in the motivic context over C. He uses the motivic May spectral sequence to compute the cohomology of the motivic Steenrod algebra over C through the 70-stem. He then uses the motivic Adams spectral sequence to obtain motivic stable homotopy groups through the 59-stem. He also describes the complete calculation to the 65-stem, but defers the proofs in this range to forthcoming publications. In addition to finding all Adams differentials, the author also resolves all hidden extensions by 2, η, and ν through the 59-stem, except for a few carefully enumerated exceptions that remain unknown. The analogous classical stable homotopy groups are easy consequences. The author also computes the motivic stable homotopy groups of the cofiber of the motivic element τ. This computation is essential for resolving hidden extensions in the Adams spectral sequence. He shows that the homotopy groups of the cofiber of τ are the same as the E2-page of the classical Adams-Novikov spectral sequence. This allows him to compute the classical Adams-Novikov spectral sequence, including differentials and hidden extensions, in a larger range than was previously known.
Formal Geometry And Bordism Operations
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Author : Eric Peterson
language : en
Publisher: Cambridge University Press
Release Date : 2019
Formal Geometry And Bordism Operations written by Eric Peterson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Mathematics categories.
Delivers a broad, conceptual introduction to chromatic homotopy theory, focusing on contact with arithmetic and algebraic geometry.
Motivic Homotopy Theory
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Author : Bjørn Ian Dundas
language : en
Publisher: Springer Science & Business Media
Release Date : 2007
Motivic Homotopy Theory written by Bjørn Ian Dundas and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
This book is based on lectures given at a summer school on motivic homotopy theory at the Sophus Lie Centre in Nordfjordeid, Norway, in August 2002. Vladimir Voevodsky is one of the founders of the theory and received the Fields medal for his work.
Stable Homotopy And Generalised Homology
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Author : John Frank Adams
language : en
Publisher: University of Chicago Press
Release Date : 1974
Stable Homotopy And Generalised Homology written by John Frank Adams and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Mathematics categories.
J. Frank Adams, the founder of stable homotopy theory, gave a lecture series at the University of Chicago in 1967, 1970, and 1971, the well-written notes of which are published in this classic in algebraic topology. The three series focused on Novikov's work on operations in complex cobordism, Quillen's work on formal groups and complex cobordism, and stable homotopy and generalized homology. Adams's exposition of the first two topics played a vital role in setting the stage for modern work on periodicity phenomena in stable homotopy theory. His exposition on the third topic occupies the bulk of the book and gives his definitive treatment of the Adams spectral sequence along with many detailed examples and calculations in KU-theory that help give a feel for the subject.
Odd Primary Infinite Families In Stable Homotopy Theory
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Author : Ralph L. Cohen
language : en
Publisher: American Mathematical Soc.
Release Date : 1981
Odd Primary Infinite Families In Stable Homotopy Theory written by Ralph L. Cohen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Mathematics categories.
Addresses issues with odd primary infinite families in stable homotopy theory.
A Concise Course In Algebraic Topology
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Author : J. P. May
language : en
Publisher: University of Chicago Press
Release Date : 1999-09
A Concise Course In Algebraic Topology written by J. P. May and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-09 with Mathematics categories.
Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups. This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields. J. Peter May's approach reflects the enormous internal developments within algebraic topology over the past several decades, most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final four chapters provide sketches of substantial areas of algebraic topology that are normally omitted from introductory texts, and the book concludes with a list of suggested readings for those interested in delving further into the field.
Equivariant Stable Homotopy Theory And The Kervaire Invariant Problem
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Author : Michael A. Hill
language : en
Publisher: Cambridge University Press
Release Date : 2021-07-29
Equivariant Stable Homotopy Theory And The Kervaire Invariant Problem written by Michael A. Hill and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-29 with Mathematics categories.
A complete and definitive account of the authors' resolution of the Kervaire invariant problem in stable homotopy theory.