Author : F. R. Cohen
Publisher : Springer
Page : 501 pages
File Size : 27,31 MB
Release : 2007-01-05
Category : Mathematics
ISBN : 3540379851
[PDF] The Homology Of Iterated Loop Spaces eBook
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The Homology of Iterated Loop Spaces
Author : F. R. Cohen
Publisher :
Page : 508 pages
File Size : 40,39 MB
Release : 2014-01-15
Category :
ISBN : 9783662209226
The Homology of Iterated Loop Spaces
Author : Frederick Ronald Cohen
Publisher : Springer
Page : 490 pages
File Size : 45,81 MB
Release : 1976
Category : Classifying spaces
ISBN : 9780387079844
The Geometry of Iterated Loop Spaces
Author : J.P. May
Publisher : Springer
Page : 184 pages
File Size : 29,62 MB
Release : 2006-11-15
Category : Mathematics
ISBN : 3540376038
The Homology of Iterated Loop Spaces
Author : Christopher J. Preston
Publisher :
Page : 200 pages
File Size : 43,67 MB
Release : 1976
Category : Classifying spaces
ISBN : 9780387078526
Algebraic Methods in Unstable Homotopy Theory
Author : Joseph Neisendorfer
Publisher : Cambridge University Press
Page : 575 pages
File Size : 46,53 MB
Release : 2010-02-18
Category : Mathematics
ISBN : 1139482599
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.
The Geometry of Iterated Loop Spaces
Author : J. Peter May
Publisher :
Page : 175 pages
File Size : 29,28 MB
Release : 1972
Category : Categories (Mathematics)
ISBN :
The Homology of Hopf Spaces
Author : R.M. Kane
Publisher : North Holland
Page : 504 pages
File Size : 23,79 MB
Release : 1988-08
Category : Mathematics
ISBN :
This exposition of the theory of finite Hopf spaces details the development of the subject over the last thirty years, with the homology of such spaces as its main theme. The three chief areas of study in the volume are: - The study of finite H-spaces with torsion free integral homology. - The study of finite H-spaces with homology torsion. - The construction of finite H-spaces.
Lecture Notes in Algebraic Topology
Author : James F. Davis
Publisher : American Mathematical Society
Page : 385 pages
File Size : 45,31 MB
Release : 2023-05-22
Category : Mathematics
ISBN : 1470473682
The amount of algebraic topology a graduate student specializing in topology must learn can be intimidating. Moreover, by their second year of graduate studies, students must make the transition from understanding simple proofs line-by-line to understanding the overall structure of proofs of difficult theorems. To help students make this transition, the material in this book is presented in an increasingly sophisticated manner. It is intended to bridge the gap between algebraic and geometric topology, both by providing the algebraic tools that a geometric topologist needs and by concentrating on those areas of algebraic topology that are geometrically motivated. Prerequisites for using this book include basic set-theoretic topology, the definition of CW-complexes, some knowledge of the fundamental group/covering space theory, and the construction of singular homology. Most of this material is briefly reviewed at the beginning of the book. The topics discussed by the authors include typical material for first- and second-year graduate courses. The core of the exposition consists of chapters on homotopy groups and on spectral sequences. There is also material that would interest students of geometric topology (homology with local coefficients and obstruction theory) and algebraic topology (spectra and generalized homology), as well as preparation for more advanced topics such as algebraic $K$-theory and the s-cobordism theorem. A unique feature of the book is the inclusion, at the end of each chapter, of several projects that require students to present proofs of substantial theorems and to write notes accompanying their explanations. Working on these projects allows students to grapple with the “big picture”, teaches them how to give mathematical lectures, and prepares them for participating in research seminars. The book is designed as a textbook for graduate students studying algebraic and geometric topology and homotopy theory. It will also be useful for students from other fields such as differential geometry, algebraic geometry, and homological algebra. The exposition in the text is clear; special cases are presented over complex general statements.
Geometry of Loop Spaces and the Cobar Construction
Author : Hans J. Baues
Publisher : American Mathematical Soc.
Page : 194 pages
File Size : 21,17 MB
Release : 1980
Category : Mathematics
ISBN : 0821822306
The homology of iterated loop spaces [capital Greek]Omega [superscript]n [italic]X has always been a problem of major interest because it gives some insight into the homotopy of [italic]X, among other things. Therefore, if [italic]X is a CW-complex, one has been interested in small CW models for [capital Greek]Omega [superscript]n [italic]X in order to compute the cellular chain complex. The author proves a very general model theorem from which he can derive models, in addition to very technical proofs of the model theorem for several other models.