Cohomology Operations And Applications In Homotopy Theory
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Cohomology Operations And Applications In Homotopy Theory
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Author : Robert E. Mosher
language : en
Publisher: Courier Corporation
Release Date : 2008-01-01
Cohomology Operations And Applications In Homotopy Theory written by Robert E. Mosher and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-01 with Mathematics categories.
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.
Secondary Cohomology Operations
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Author : John R. Harper
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Secondary Cohomology Operations written by John R. Harper 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 2002 with Homology theory categories.
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.
Algebraic Topology Homotopy And Homology
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Author : Robert M. Switzer
language : en
Publisher: Springer
Release Date : 2017-12-01
Algebraic Topology Homotopy And Homology written by Robert M. Switzer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-01 with Mathematics categories.
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
Introduction To Homotopy Theory
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Author : Paul Selick
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Introduction To Homotopy Theory written by Paul Selick 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 2008 with Mathematics categories.
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.
Homotopy Theory An Introduction To Algebraic Topology
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Author :
language : en
Publisher: Academic Press
Release Date : 1975-11-12
Homotopy Theory An Introduction To Algebraic Topology written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975-11-12 with Mathematics categories.
Homotopy Theory: An Introduction to Algebraic Topology
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.
Homotopy Theory And Its Applications
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Author : Alejandro Adem
language : en
Publisher: American Mathematical Soc.
Release Date : 1995
Homotopy Theory And Its Applications written by Alejandro Adem 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 1995 with Homotopy theory categories.
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.
Algebraic Topology
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Author : Edwin H. Spanier
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Algebraic Topology written by Edwin H. Spanier 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 2012-12-06 with Mathematics categories.
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.
The Algebra Of Secondary Cohomology Operations
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Author : Hans-Joachim Baues
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-06-12
The Algebra Of Secondary Cohomology Operations written by Hans-Joachim Baues 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 2006-06-12 with Mathematics categories.
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.
Cohomology Operations
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Author : Norman Earl Steenrod
language : en
Publisher: Princeton University Press
Release Date : 1962
Cohomology Operations written by Norman Earl Steenrod and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1962 with Homology theory categories.