Homotopy Theory and Models: Based on Lectures held at a DMV Seminar in Blaubeuren by H.J. Baues, S. Halperin and J.-M. Lemaire

Homotopy Theory and Models: Based on Lectures held at a DMV Seminar in Blaubeuren by H.J. Baues, S. Halperin and J.-M. Lemaire

Paperback(1995)

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Product Details

ISBN-13: 9783764351854
Publisher: Birkhauser Basel
Publication date: 03/27/1995
Series: Oberwolfach Seminars Series , #24
Edition description: 1995
Pages: 117
Product dimensions: 6.69(w) x 9.61(h) x (d)

Table of Contents

1: Basic Homotopy Theory.- §1. Homotopy.- §2. Cofibrations and fibrations.- 2: Homology and Homotopy Decomposition of Simply Connected Spaces.- §1. Eckmann-Hilton duality.- §2. Homology and homotopy decompositions.- §3. Application: Classification of 2-stage spaces.- 3: Cofibration Categories.- §1. Basic definitions.- §2. Homotopy in a cofibration category.- §3. Properties of cofibration categories.- §4. Properties of cofibrant models.- §5. The homotopy category as a localization.- 4: Algebraic Examples of Cofibration Categories.- §1. The category CDA.- §2. The category Chain+.- §3. The category DA.- §4. The category DL.- 5: The Rational Homotopy Category of Simply Connected Spaces.- §1. The category of rational spaces.- §2. Quillen’s model category.- §3. Sullivan’s model theory.- §4. Some easy applications.- Appendix: Relations between the Various Models of a Space.- A.1. A functor between DL and CDA.- A.2. Models over—/p?.- A.3. Sullivan Models.- 6: Attaching Cells in Topology and Algebra.- §1. Algebraic models of spaces with a cell attached.- §2. Inertia.- 7: Elliptic Spaces.- §1. Finiteness of the formal dimension.- §2. Elliptic models.- §3. Some equalities and inequalities.- §4. Topological interpretation.- 8: Non Elliptic Finite C.W.-Complexes.- §1. Homotopy invariants of spaces.- §2. Sullivan models and the (algebraic) Lusternik-Schnirelmann category.- §3. Lie algebras of finite depth.- §4. The mapping theorem.- §5. Proof of Theorem 0.1.- 9: Towards Integral Algebraic Models of Homotopy Types.- §1. Introduction and general problem.- §2. Algebraic description of the integral homotopy types in dimension 4.- §3. Algebraic description of the integral homotopy types in dimension N.

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