Stable And Unstable Homotopy

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Stable and Unstable Homotopy

Author : William G. Dwyer
Publisher : American Mathematical Soc.
Page : 326 pages
File Size : 40,9 Mb
Release : 1998
Category : Mathematics
ISBN : 9780821808245

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Stable and Unstable Homotopy by William G. Dwyer Pdf

This volume presents the proceedings of workshops on stable homotopy theory and on unstable homotopy theory held at The Fields Institute as part of the homotopy program during the year 1996. The papers in the volume describe current research in the subject, and all included works were refereed. Rather than being a summary of work to be published elsewhere, each paper is the unique source for the new material it contains. The book contains current research from international experts in the subject area, and presents open problems with directions for future research.

Analyse différentielle

Author : Barry Mazur,R. Milgram,Valentin Poenaru
Publisher : Unknown
Page : 339 pages
File Size : 50,9 Mb
Release : 1974
Category : Abelian varieties
ISBN : 0387066551

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Analyse différentielle by Barry Mazur,R. Milgram,Valentin Poenaru Pdf

Complex Cobordism and Stable Homotopy Groups of Spheres

Author : Douglas C. Ravenel
Publisher : American Mathematical Society
Page : 417 pages
File Size : 52,8 Mb
Release : 2023-02-09
Category : Mathematics
ISBN : 9781470472931

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Complex Cobordism and Stable Homotopy Groups of Spheres by Douglas C. Ravenel Pdf

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.

Groups of Homotopy Spheres, I

Author : M a Kervaire,John W Milnor
Publisher : Legare Street Press
Page : 0 pages
File Size : 44,9 Mb
Release : 2023-07-18
Category : Electronic
ISBN : 1019386339

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Groups of Homotopy Spheres, I by M a Kervaire,John W Milnor Pdf

This book is a groundbreaking work in the field of topology, exploring the properties of homotopy spheres and the various groups that can be derived from them. With detailed proofs and rigorous analysis, this book is a must-read for anyone interested in topology or higher mathematics. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Nilpotence and Periodicity in Stable Homotopy Theory

Author : Douglas C. Ravenel
Publisher : Princeton University Press
Page : 228 pages
File Size : 54,9 Mb
Release : 1992-11-08
Category : Mathematics
ISBN : 069102572X

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Nilpotence and Periodicity in Stable Homotopy Theory by Douglas C. Ravenel Pdf

Nilpotence and Periodicity in Stable Homotopy Theory describes some major advances made in algebraic topology in recent years, centering on the nilpotence and periodicity theorems, which were conjectured by the author in 1977 and proved by Devinatz, Hopkins, and Smith in 1985. During the last ten years a number of significant advances have been made in homotopy theory, and this book fills a real need for an up-to-date text on that topic. Ravenel's first few chapters are written with a general mathematical audience in mind. They survey both the ideas that lead up to the theorems and their applications to homotopy theory. The book begins with some elementary concepts of homotopy theory that are needed to state the problem. This includes such notions as homotopy, homotopy equivalence, CW-complex, and suspension. Next the machinery of complex cobordism, Morava K-theory, and formal group laws in characteristic p are introduced. The latter portion of the book provides specialists with a coherent and rigorous account of the proofs. It includes hitherto unpublished material on the smash product and chromatic convergence theorems and on modular representations of the symmetric group.

Algebraic Methods in Unstable Homotopy Theory

Author : Joseph Neisendorfer
Publisher : Cambridge University Press
Page : 575 pages
File Size : 44,6 Mb
Release : 2010-02-18
Category : Mathematics
ISBN : 9781139482592

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Algebraic Methods in Unstable Homotopy Theory by Joseph Neisendorfer Pdf

The most modern and thorough treatment of unstable homotopy theory available. The focus is on those methods from algebraic topology which are needed in the presentation of results, proven by Cohen, Moore, and the author, on the exponents of homotopy groups. The author introduces various aspects of unstable homotopy theory, including: homotopy groups with coefficients; localization and completion; the Hopf invariants of Hilton, James, and Toda; Samelson products; homotopy Bockstein spectral sequences; graded Lie algebras; differential homological algebra; and the exponent theorems concerning the homotopy groups of spheres and Moore spaces. This book is suitable for a course in unstable homotopy theory, following a first course in homotopy theory. It is also a valuable reference for both experts and graduate students wishing to enter the field.

Algebraic and Differential Topology of Robust Stability

Author : Edmond A. Jonckheere
Publisher : Oxford University Press
Page : 625 pages
File Size : 40,6 Mb
Release : 1997-05-29
Category : Mathematics
ISBN : 9780195357684

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Algebraic and Differential Topology of Robust Stability by Edmond A. Jonckheere Pdf

In this book, two seemingly unrelated fields -- algebraic topology and robust control -- are brought together. The book develops algebraic/differential topology from an application-oriented point of view. The book takes the reader on a path starting from a well-motivated robust stability problem, showing the relevance of the simplicial approximation theorem and how it can be efficiently implemented using computational geometry. The simplicial approximation theorem serves as a primer to more serious topological issues such as the obstruction to extending the Nyquist map, K-theory of robust stabilization, and eventually the differential topology of the Nyquist map, culminating in the explanation of the lack of continuity of the stability margin relative to rounding errors. The book is suitable for graduate students in engineering and/or applied mathematics, academic researchers and governmental laboratories.

The Unstable Adams Spectral Sequence for Free Iterated Loop Spaces

Author : Robert J. Wellington
Publisher : American Mathematical Soc.
Page : 237 pages
File Size : 45,8 Mb
Release : 1982
Category : Adams spectral sequences
ISBN : 9780821822586

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The Unstable Adams Spectral Sequence for Free Iterated Loop Spaces by Robert J. Wellington Pdf

The semi-stable homotopy groups of a topological space [italic]X are the unstable homotopy groups [lowercase Greek]Pi [subscript]*[capital Greek]Sigma[superscript]n[italic]X, [italic]n [greater than symbol] 0, of the suspensions of [italic]X. This monograph is concerned with computing these semi-stable homotopy groups using the unstable Adams spectral sequence for the free iterated loop spaces [capital Greek]Omega[superscript italic]n [capital Greek]Sigma[superscript italic]n [italic]X generated by [italic]X.

Recent Progress in Homotopy Theory

Author : Donald M. Davis
Publisher : American Mathematical Soc.
Page : 424 pages
File Size : 45,7 Mb
Release : 2002
Category : Mathematics
ISBN : 9780821828014

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Recent Progress in Homotopy Theory by Donald M. Davis Pdf

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.

Homotopy Theory and Its Applications

Author : Alejandro Adem,R. James Milgram,Douglas C. Ravenel
Publisher : American Mathematical Soc.
Page : 250 pages
File Size : 51,8 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821803059

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Homotopy Theory and Its Applications by Alejandro Adem,R. James Milgram,Douglas C. Ravenel Pdf

This book is the result of a conference held to examine developments in homotopy theory in honor of Samuel Gitler in July 1993 (Cocoyoc, Mexico). It includes several research papers and three expository papers on various topics in homotopy theory. The research papers discuss the following: BL application of homotopy theory to group theory BL fiber bundle theory BL homotopy theory The expository papers consider the following topics: BL the Atiyah-Jones conjecture (by C. Boyer) BL classifying spaces of finite groups (by J. Martino) BL instanton moduli spaces (by J. Milgram) Homotopy Theory and Its Applications offers a distinctive account of how homotopy theoretic methods can be applied to a variety of interesting problems.

Group Representations: Cohomology, Group Actions and Topology

Author : Alejandro Adem,Representations Summer Research Institute on Cohomology
Publisher : American Mathematical Soc.
Page : 549 pages
File Size : 41,8 Mb
Release : 1998
Category : Finite groups
ISBN : 9780821806586

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Group Representations: Cohomology, Group Actions and Topology by Alejandro Adem,Representations Summer Research Institute on Cohomology Pdf

This volume combines contributions in topology and representation theory that reflect the increasingly vigorous interactions between these areas. Topics such as group theory, homotopy theory, cohomology of groups, and modular representations are covered. All papers have been carefully refereed and offer lasting value.

Stable Homotopy

Author : Joel M. Cohen
Publisher : Springer
Page : 200 pages
File Size : 49,7 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540363934

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Stable Homotopy by Joel M. Cohen Pdf

Global Homotopy Theory

Author : Stefan Schwede
Publisher : Cambridge University Press
Page : 847 pages
File Size : 53,9 Mb
Release : 2018-09-06
Category : Mathematics
ISBN : 9781108425810

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Global Homotopy Theory by Stefan Schwede Pdf

A comprehensive, self-contained approach to global equivariant homotopy theory, with many detailed examples and sample calculations.

Homotopy Theory via Algebraic Geometry and Group Representations

Author : Mark E. Mahowald
Publisher : American Mathematical Soc.
Page : 394 pages
File Size : 49,5 Mb
Release : 1998
Category : Mathematics
ISBN : 9780821808054

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Homotopy Theory via Algebraic Geometry and Group Representations by Mark E. Mahowald Pdf

The academic year 1996-97 was designated as a special year in Algebraic Topology at Northwestern University (Evanston, IL). In addition to guest lecturers and special courses, an international conference was held entitled "Current trends in algebraic topology with applications to algebraic geometry and physics". The series of plenary lectures included in this volume indicate the great breadth of the conference and the lively interaction that took place among various areas of mathematics. Original research papers were submitted, and all submissions were refereed to the usual journal standards.