Modern classical homotopy theory
"The core of classical homotopy theory is a body of ideas and theorems that emerged in the 1950s and was later largely codified in the notion of a model category. This core includes the notions of fibration and cofibration; CW complexes; long fiber and cofiber sequences; loop spaces and suspensions; and so on. Brown's representability theorems show that homology and cohomology are also contained in classical homotopy theory. This text develops classical homotopy theory from a modern point of vi…
Read More ↓Title Statements
- Full title :Modern classical homotopy theory / Jeffrey Strom.
Summary
"The core of classical homotopy theory is a body of ideas and theorems that emerged in the 1950s and was later largely codified in the notion of a model category. This core includes the notions of fibration and cofibration; CW complexes; long fiber and cofiber sequences; loop spaces and suspensions; and so on. Brown's representability theorems show that homology and cohomology are also contained in classical homotopy theory. This text develops classical homotopy theory from a modern point of view, meaning that the exposition is informed by the theory of model categories and that homotopy limits and colimits play central roles. The exposition is guided by the principle that it is generally preferable to prove topological results using topology (rather than algebra). The language and basic theory of homotopy limits and colimits make it possible to penetrate deep into the subject with just the rudiments of algebra. The text does reach advanced territory, including the Steenrod algebra, Bott periodicity, localization, the Exponent Theorem of Cohen, Moore, and Neisendorfer, and Miller's Theorem on the Sullivan Conjecture. Thus the reader is given the tools needed to understand and participate in research at (part of) the current frontier of homotopy theory. Proofs are not provided outright. Rather, they are presented in the form of directed problem sets. To the expert, these read as terse proofs; to novices they are challenges that draw them in and help them to thoroughly understand the arguments." -- Publisher.
Read More ↓Edition Statements
- Publication Date:©2011.
Publication Statements
- Publisher(s):American mathematical Society
- Place of Publication:Providence, R.I
- Language:eng
- Publication Date:©2011.
The Physical Object
- Description:xxi, 835 pages : : illustrations ; : 27 cm.
Edition Identifiers
- ISBN:9780821852866, 0821852868
- oclc:ocn723142884
- LC Classification:QA612.7
- Dewey Decimal:514/.24
Table of Contents
Categories and functors -- Limits and colimits -- Categories of spaces -- Homotopy -- Cofibrations and fibrations -- Homotopy limits and colimits -- Homotopy pushout and pullback squares -- Tools and techniques -- Topics and examples -- Model categories -- The concept of dimension in homotopy theory -- Subdivision of disks -- The local nature of fibrations -- Pullbacks of cofibrations -- Related topics -- Constructions of spaces and maps -- Understanding suspension -- Comparing pushouts and pullbacks -- Some computations in homotopy theory -- Further topics -- Cohomology -- Homology -- Cohomology operations -- Chain complexes -- Topics, problems and projects -- The Wang sequence -- Cohomology of filtered spaces -- The Serre filtration of a fibration -- Application : incompressibility -- The spectral sequence of a filtered space -- The Leray-Serre spectral sequence -- Application : Bott periodicity -- Using the Leray-Serre spectral sequence -- Localization and completion -- Exponents for homotopy groups -- Classes of spaces -- Miller's theorem.
Read More ↓Subjects
Writers
More from this Series
No reviews yet. Be the first to rate this work.
Related Works
more →
Files & Downloads
-
Modern Classical Homotopy Theory -- (.djvu)
DJVU · 7.0 MB · updated -
Modern Classical Homotopy Theory -- (.pdf)
PDF · 7.7 MB · updated -
Modern classical homotopy theory -- (.djvu)
DJVU · 7.1 MB · updated -
Modern classical homotopy theory -- (.pdf)
PDF · 5.0 MB · updated
Rate & Review