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Author : William Gerard Dwyer
Publisher :
ISBN 13 :
Total Pages : 52 pages
Book Rating : 4.:/5 (145 download)
Download or read book Strong Convergence of the Eilenberg-Moore Spectral Sequence written by William Gerard Dwyer and published by . This book was released on 1973 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jaume Aguade
Publisher : Birkhäuser
ISBN 13 : 3034883129
Total Pages : 413 pages
Book Rating : 4.0/5 (348 download)
Download or read book Cohomological Methods in Homotopy Theory written by Jaume Aguade and published by Birkhäuser. This book was released on 2012-12-06 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a collection of articles summarizing the state of knowledge in a large portion of modern homotopy theory. A call for articles was made on the occasion of an emphasis semester organized by the Centre de Recerca Matemtica in Bellaterra (Barcelona) in 1998. The main topics treated in the book include abstract features of stable and unstable homotopy, homotopical localizations, p-compact groups, H-spaces, classifying spaces for proper actions, cohomology of discrete groups, K-theory and other generalized cohomology theories, configuration spaces, and Lusternik-Schnirelmann category. The book is addressed to all mathematicians interested in homotopy theory and in geometric aspects of group theory. New research directions in topology are highlighted. Moreover, this informative and educational book serves as a welcome reference for many new results and recent methods.
Author : John McCleary
Publisher : Cambridge University Press
ISBN 13 : 0521567599
Total Pages : 579 pages
Book Rating : 4.5/5 (215 download)
Download or read book A User's Guide to Spectral Sequences written by John McCleary and published by Cambridge University Press. This book was released on 2001 with total page 579 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spectral sequences are among the most elegant and powerful methods of computation in mathematics. This book describes some of the most important examples of spectral sequences and some of their most spectacular applications. The first part treats the algebraic foundations for this sort of homological algebra, starting from informal calculations. The heart of the text is an exposition of the classical examples from homotopy theory, with chapters on the Leray-Serre spectral sequence, the Eilenberg-Moore spectral sequence, the Adams spectral sequence, and, in this new edition, the Bockstein spectral sequence. The last part of the book treats applications throughout mathematics, including the theory of knots and links, algebraic geometry, differential geometry and algebra. This is an excellent reference for students and researchers in geometry, topology, and algebra.
Author : Akira Kōno
Publisher : American Mathematical Soc.
ISBN 13 : 9780821835142
Total Pages : 276 pages
Book Rating : 4.8/5 (351 download)
Download or read book Generalized Cohomology written by Akira Kōno and published by American Mathematical Soc.. This book was released on 2006 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aims to give an exposition of generalized (co)homology theories that can be read by a group of mathematicians who are not experts in algebraic topology. This title starts with basic notions of homotopy theory, and introduces the axioms of generalized (co)homology theory. It also discusses various types of generalized cohomology theories.
Author : Larry Smith
Publisher : Springer
ISBN 13 : 354036286X
Total Pages : 149 pages
Book Rating : 4.5/5 (43 download)
Download or read book Lectures on the Eilenberg-Moore Spectral Sequence written by Larry Smith and published by Springer. This book was released on 2006-11-15 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Yves Felix
Publisher : Springer Science & Business Media
ISBN 13 : 0387950680
Total Pages : 589 pages
Book Rating : 4.3/5 (879 download)
Download or read book Rational Homotopy Theory written by Yves Felix and published by Springer Science & Business Media. This book was released on 2001 with total page 589 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a long awaited book on rational homotopy theory which contains all the main theorems with complete proofs, and more elementary proofs for many results that were proved ten or fifteen years ago. The authors added a frist section on classical algebraic topology to make the book accessible to students with only little background in algebraic topology.
Author : Brian A. Munson
Publisher : Cambridge University Press
ISBN 13 : 1107030250
Total Pages : 649 pages
Book Rating : 4.1/5 (7 download)
Download or read book Cubical Homotopy Theory written by Brian A. Munson and published by Cambridge University Press. This book was released on 2015-10-06 with total page 649 pages. Available in PDF, EPUB and Kindle. Book excerpt: A modern, example-driven introduction to cubical diagrams and related topics such as homotopy limits and cosimplicial spaces.
Author : J. P. May
Publisher : University of Chicago Press
ISBN 13 : 0226511782
Total Pages : 544 pages
Book Rating : 4.2/5 (265 download)
Download or read book More Concise Algebraic Topology written by J. P. May and published by University of Chicago Press. This book was released on 2012-02 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: With firm foundations dating only from the 1950s, algebraic topology is a relatively young area of mathematics. There are very few textbooks that treat fundamental topics beyond a first course, and many topics now essential to the field are not treated in any textbook. J. Peter May’s A Concise Course in Algebraic Topology addresses the standard first course material, such as fundamental groups, covering spaces, the basics of homotopy theory, and homology and cohomology. In this sequel, May and his coauthor, Kathleen Ponto, cover topics that are essential for algebraic topologists and others interested in algebraic topology, but that are not treated in standard texts. They focus on the localization and completion of topological spaces, model categories, and Hopf algebras. The first half of the book sets out the basic theory of localization and completion of nilpotent spaces, using the most elementary treatment the authors know of. It makes no use of simplicial techniques or model categories, and it provides full details of other necessary preliminaries. With these topics as motivation, most of the second half of the book sets out the theory of model categories, which is the central organizing framework for homotopical algebra in general. Examples from topology and homological algebra are treated in parallel. A short last part develops the basic theory of bialgebras and Hopf algebras.
Author : Birgit Richter
Publisher : Cambridge University Press
ISBN 13 : 1108847625
Total Pages : 402 pages
Book Rating : 4.1/5 (88 download)
Download or read book From Categories to Homotopy Theory written by Birgit Richter and published by Cambridge University Press. This book was released on 2020-04-16 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Category theory provides structure for the mathematical world and is seen everywhere in modern mathematics. With this book, the author bridges the gap between pure category theory and its numerous applications in homotopy theory, providing the necessary background information to make the subject accessible to graduate students or researchers with a background in algebraic topology and algebra. The reader is first introduced to category theory, starting with basic definitions and concepts before progressing to more advanced themes. Concrete examples and exercises illustrate the topics, ranging from colimits to constructions such as the Day convolution product. Part II covers important applications of category theory, giving a thorough introduction to simplicial objects including an account of quasi-categories and Segal sets. Diagram categories play a central role throughout the book, giving rise to models of iterated loop spaces, and feature prominently in functor homology and homology of small categories.
Author : Michael Slack
Publisher : American Mathematical Soc.
ISBN 13 : 0821825143
Total Pages : 125 pages
Book Rating : 4.8/5 (218 download)
Download or read book A Classification Theorem for Homotopy Commutative $H$-Spaces with Finitely Generated $\bmod 2$ Cohomology Rings written by Michael Slack and published by American Mathematical Soc.. This book was released on 1991 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is shown that a 2-connected homotopy commutative H-space with associative mod 2 homology ring and finitely generated mod 2 cohomology ring has acyclic mod 2 cohomology. This implies that a connected, homotopy commutative, homotopy associative H-space with finitely generated mod 2 cohomology ring is mod 2 homotopy equivalent to a product of Eilenberg-MacLane spaces, giving a complete classification of such spaces localized at the prime 2.
Author : Luchezar L. Avramov
Publisher : American Mathematical Soc.
ISBN 13 : 0821838148
Total Pages : 352 pages
Book Rating : 4.8/5 (218 download)
Download or read book Interactions between Homotopy Theory and Algebra written by Luchezar L. Avramov and published by American Mathematical Soc.. This book was released on 2007 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on talks presented at the Summer School on Interactions between Homotopy theory and Algebra held at the University of Chicago in the summer of 2004. The goal of this book is to create a resource for background and for current directions of research related to deep connections between homotopy theory and algebra, including algebraic geometry, commutative algebra, and representation theory. The articles in this book are aimed at the audience of beginning researchers with varied mathematical backgrounds and have been written with both the quality of exposition and the accessibility to novices in mind.
Author : James Earl Kettner
Publisher :
ISBN 13 :
Total Pages : 142 pages
Book Rating : 4.:/5 (3 download)
Download or read book The Generalized Eilenberg-Moore Spectral Sequence written by James Earl Kettner and published by . This book was released on 1972 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : J. Peter May
Publisher : American Mathematical Soc.
ISBN 13 : 0821839225
Total Pages : 456 pages
Book Rating : 4.8/5 (218 download)
Download or read book Parametrized Homotopy Theory written by J. Peter May and published by American Mathematical Soc.. This book was released on 2006 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops rigorous foundations for parametrized homotopy theory, which is the algebraic topology of spaces and spectra that are continuously parametrized by the points of a base space. It also begins the systematic study of parametrized homology and cohomology theories. The parametrized world provides the natural home for many classical notions and results, such as orientation theory, the Thom isomorphism, Atiyah and Poincare duality, transfer maps, the Adams and Wirthmuller isomorphisms, and the Serre and Eilenberg-Moore spectral sequences. But in addition to providing a clearer conceptual outlook on these classical notions, it also provides powerful methods to study new phenomena, such as twisted $K$-theory, and to make new constructions, such as iterated Thom spectra. Duality theory in the parametrized setting is particularly illuminating and comes in two flavors. One allows the construction and analysis of transfer maps, and a quite different one relates parametrized homology to parametrized cohomology. The latter is based formally on a new theory of duality in symmetric bicategories that is of considerable independent interest. The text brings together many recent developments in homotopy theory. It provides a highly structured theory of parametrized spectra, and it extends parametrized homotopy theory to the equivariant setting. The theory of topological model categories is given a more thorough treatment than is available in the literature. This is used, together with an interesting blend of classical methods, to resolve basic foundational problems that have no nonparametrized counterparts.
Author : John McCleary
Publisher :
ISBN 13 :
Total Pages : 448 pages
Book Rating : 4.3/5 (91 download)
Download or read book User's Guide to Spectral Sequences written by John McCleary and published by . This book was released on 1985 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Lionel Schwartz
Publisher : University of Chicago Press
ISBN 13 : 9780226742038
Total Pages : 244 pages
Book Rating : 4.7/5 (42 download)
Download or read book Unstable Modules Over the Steenrod Algebra and Sullivan's Fixed Point Set Conjecture written by Lionel Schwartz and published by University of Chicago Press. This book was released on 1994-07-15 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive account of one of the main directions of algebraic topology, this book focuses on the Sullivan conjecture and its generalizations and applications. Lionel Schwartz collects here for the first time some of the most innovative work on the theory of modules over the Steenrod algebra, including ideas on the Segal conjecture, work from the late 1970s by Adams and Wilkerson, and topics in algebraic group representation theory. This course-tested book provides a valuable reference for algebraic topologists and includes foundational material essential for graduate study.
Author : John Rognes
Publisher : American Mathematical Soc.
ISBN 13 : 0821840762
Total Pages : 154 pages
Book Rating : 4.8/5 (218 download)
Download or read book Galois Extensions of Structured Ring Spectra/Stably Dualizable Groups written by John Rognes and published by American Mathematical Soc.. This book was released on 2008 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author introduces the notion of a Galois extension of commutative $S$-algebras ($E_\infty$ ring spectra), often localized with respect to a fixed homology theory. There are numerous examples, including some involving Eilenberg-Mac Lane spectra of commutative rings, real and complex topological $K$-theory, Lubin-Tate spectra and cochain $S$-algebras. He establishes the main theorem of Galois theory in this generality. Its proof involves the notions of separable and etale extensions of commutative $S$-algebras, and the Goerss-Hopkins-Miller theory for $E_\infty$ mapping spaces. He shows that the global sphere spectrum $S$ is separably closed, using Minkowski's discriminant theorem, and he estimates the separable closure of its localization with respect to each of the Morava $K$-theories. He also defines Hopf-Galois extensions of commutative $S$-algebras and studies the complex cobordism spectrum $MU$ as a common integral model for all of the local Lubin-Tate Galois extensions. The author extends the duality theory for topological groups from the classical theory for compact Lie groups, via the topological study by J. R. Klein and the $p$-complete study for $p$-compact groups by T. Bauer, to a general duality theory for stably dualizable groups in the $E$-local stable homotopy category, for any spectrum $E$.
Author : Martin C. Tangora
Publisher : American Mathematical Soc.
ISBN 13 : 0821851624
Total Pages : 504 pages
Book Rating : 4.8/5 (218 download)
Download or read book Algebraic Topology: Oaxtepec 1991 written by Martin C. Tangora and published by American Mathematical Soc.. This book was released on 1993 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of twenty-nine articles contributed by participants of the International Conference in Algebraic Topology held in July 1991 in Mexico. In addition to papers on current research, there are several surveys and expositions on the work of Mark Mahowald, whose sixtieth birthday was celebrated during the conference. The conference was truly international, with over 130 mathematicians from fifteen countries. It ended with a spectacular total eclipse of the sun, a photograph of which appears as the frontispiece. The papers range over much of algebraic topology and cross over into related areas, such as K theory, representation theory, and Lie groups. Also included is a chart of the Adams spectral sequence and a bibliography of Mahowald's publications.
