Cohomology Operations And Applications In Homotopy Theory

Author : Robert E. Mosher,Martin C. Tangora
Publisher : Courier Corporation
Page : 226 pages
File Size : 41,6 Mb
Release : 2008-01-01
Category : Mathematics
ISBN : 9780486466644

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Cohomology Operations and Applications in Homotopy Theory by Robert E. Mosher,Martin C. Tangora Pdf

Cohomology operations are at the center of a major area of activity in algebraic topology. This treatment explores the single most important variety of operations, the Steenrod squares. It constructs these operations, proves their major properties, and provides numerous applications, including several different techniques of homotopy theory useful for computation. 1968 edition.

Author : John R. Harper
Publisher : American Mathematical Soc.
Page : 282 pages
File Size : 49,7 Mb
Release : 2002
Category : Homology theory
ISBN : 9780821831984

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Secondary Cohomology Operations by John R. Harper Pdf

Although the theory and applications of secondary cohomology operations are an important part of an advanced graduate-level algebraic topology course, there are few books on the subject. The AMS now fills that gap with the publication of the present volume. The author's main purpose in this book is to develop the theory of secondary cohomology operations for singular cohomology theory, which is treated in terms of elementary constructions from general homotopy theory. Among manyapplications considered are the Hopf invariant one theorem (for all primes $p$, including $p = 2$), Browder's theorem on higher Bockstein operations, and cohomology theory of Massey-Peterson fibrations. Numerous examples and exercises help readers to gain a working knowledge of the theory. A summary ofmore advanced parts of the core material is included in the first chapter. Prerequisite is basic algebraic topology, including the Steenrod operations. The book is geared toward graduate students and research mathematicians interested in algebraic topology and can be used for self-study or as a textbook for an advanced course on the topic. It is available in both hardcover and softcover editions.

Author : Hans-Joachim Baues
Publisher : Springer Science & Business Media
Page : 484 pages
File Size : 44,5 Mb
Release : 2006-06-12
Category : Mathematics
ISBN : 9783764374495

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The Algebra of Secondary Cohomology Operations by Hans-Joachim Baues Pdf

The algebra of primary cohomology operations computed by the well-known Steenrod algebra is one of the most powerful tools of algebraic topology. This book computes the algebra of secondary cohomology operations which enriches the structure of the Steenrod algebra in a new and unexpected way. The book solves a long-standing problem on the algebra of secondary cohomology operations by developing a new algebraic theory of such operations. The results have strong impact on the Adams spectral sequence and hence on the computation of homotopy groups of spheres.

Author : Anonim
Publisher : Academic Press
Page : 367 pages
File Size : 45,7 Mb
Release : 1975-11-12
Category : Mathematics
ISBN : 0080873804

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Homotopy Theory: An Introduction to Algebraic Topology by Anonim Pdf

Homotopy Theory: An Introduction to Algebraic Topology

Author : Robert M. Switzer
Publisher : Springer
Page : 541 pages
File Size : 45,6 Mb
Release : 2017-12-01
Category : Mathematics
ISBN : 9783642619236

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Algebraic Topology - Homotopy and Homology by Robert M. Switzer Pdf

From the reviews: "The author has attempted an ambitious and most commendable project. [...] The book contains much material that has not previously appeared in this format. The writing is clean and clear and the exposition is well motivated. [...] This book is, all in all, a very admirable work and a valuable addition to the literature." Mathematical Reviews

Author : Paul Selick
Publisher : American Mathematical Soc.
Page : 220 pages
File Size : 52,5 Mb
Release : 2008
Category : Mathematics
ISBN : 0821844369

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Introduction to Homotopy Theory by Paul Selick Pdf

Offers a summary for students and non-specialists who are interested in learning the basics of algebraic topology. This book covers fibrations and cofibrations, Hurewicz and cellular approximation theorems, topics in classical homotopy theory, simplicial sets, fiber bundles, Hopf algebras, and generalized homology and cohomology operations.

Author : John Frank Adams
Publisher : University of Chicago Press
Page : 384 pages
File Size : 42,6 Mb
Release : 1974
Category : Mathematics
ISBN : 9780226005249

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Stable Homotopy and Generalised Homology by John Frank Adams Pdf

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.

Author : J. Peter May,M. Cole
Publisher : American Mathematical Soc.
Page : 384 pages
File Size : 51,7 Mb
Release : 1996
Category : Mathematics
ISBN : 9780821803196

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Equivariant Homotopy and Cohomology Theory by J. Peter May,M. Cole Pdf

This volume introduces equivariant homotopy, homology, and cohomology theory, along with various related topics in modern algebraic topology. It explains the main ideas behind some of the most striking recent advances in the subject. The works begins with a development of the equivariant algebraic topology of spaces culminating in a discussion of the Sullivan conjecture that emphasizes its relationship with classical Smith theory. The book then introduces equivariant stable homotopy theory, the equivariant stable homotopy category, and the most important examples of equivariant cohomology theories. The basic machinery that is needed to make serious use of equivariant stable homotopy theory is presented next, along with discussions of the Segal conjecture and generalized Tate cohomology. Finally, the book gives an introduction to "brave new algebra", the study of point-set level algebraic structures on spectra and its equivariant applications. Emphasis is placed on equivariant complex cobordism, and related results on that topic are presented in detail.

Author : Alejandro Adem,R. James Milgram,Douglas C. Ravenel
Publisher : American Mathematical Soc.
Page : 250 pages
File Size : 54,5 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.

Author : John Harold Palmieri
Publisher : American Mathematical Soc.
Page : 193 pages
File Size : 45,5 Mb
Release : 2001
Category : Homotopy theory
ISBN : 9780821826683

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Stable Homotopy over the Steenrod Algebra by John Harold Palmieri Pdf

This title applys the tools of stable homotopy theory to the study of modules over the mod $p$ Steenrod algebra $A DEGREES{*}$. More precisely, let $A$ be the dual of $A DEGREES{*}$; then we study the category $\mathsf{stable}(A)$ of unbounded cochain complexes of injective comodules over $A$, in which the morphisms are cochain homotopy classes of maps. This category is triangulated. Indeed, it is a stable homotopy category, so we can use Brown representability, Bousfield localization, Brown-Comenetz duality, and other homotopy-theoretic tools to study it. One focus of attention is the analogue of the stable homotopy groups of spheres, which in this setting is the cohomology of $A$, $\mathrm{Ext}_A DEGREES{**}(\mathbf{F}_p, \mathbf{F}_p)$. This title also has nilpotence theorems, periodicity theorems, a convergent chromatic tower, and a nu

Author : Hans-Joachim Baues
Publisher : Springer Science & Business Media
Page : 379 pages
File Size : 54,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662113387

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Combinatorial Foundation of Homology and Homotopy by Hans-Joachim Baues Pdf

A new combinatorial foundation of the two concepts, based on a consideration of deep and classical results of homotopy theory, and an axiomatic characterization of the assumptions under which results in this field hold. Includes numerous explicit examples and applications in various fields of topology and algebra.

Author : Haynes Miller
Publisher : CRC Press
Page : 1043 pages
File Size : 52,8 Mb
Release : 2020-01-23
Category : Mathematics
ISBN : 9781351251600

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Handbook of Homotopy Theory by Haynes Miller Pdf

The Handbook of Homotopy Theory provides a panoramic view of an active area in mathematics that is currently seeing dramatic solutions to long-standing open problems, and is proving itself of increasing importance across many other mathematical disciplines. The origins of the subject date back to work of Henri Poincaré and Heinz Hopf in the early 20th century, but it has seen enormous progress in the 21st century. A highlight of this volume is an introduction to and diverse applications of the newly established foundational theory of ¥ -categories. The coverage is vast, ranging from axiomatic to applied, from foundational to computational, and includes surveys of applications both geometric and algebraic. The contributors are among the most active and creative researchers in the field. The 22 chapters by 31 contributors are designed to address novices, as well as established mathematicians, interested in learning the state of the art in this field, whose methods are of increasing importance in many other areas.

Author : Edwin H. Spanier
Publisher : Springer Science & Business Media
Page : 502 pages
File Size : 50,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468493221

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Algebraic Topology by Edwin H. Spanier Pdf

This book surveys the fundamental ideas of algebraic topology. The first part covers the fundamental group, its definition and application in the study of covering spaces. The second part turns to homology theory including cohomology, cup products, cohomology operations and topological manifolds. The final part is devoted to Homotropy theory, including basic facts about homotropy groups and applications to obstruction theory.

Author : M. Hazewinkel
Publisher : Springer
Page : 927 pages
File Size : 53,9 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781489937971

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Encyclopaedia of Mathematics by M. Hazewinkel Pdf

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
Page : 517 pages
File Size : 44,7 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9789400960008

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Encyclopaedia of Mathematics by Michiel Hazewinkel Pdf

This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathematics. It is a translation with updates and editorial comments of the Soviet Mathematical En cyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977 - 1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivision has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathe matics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, engineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.