Homotopy theory and models : based on lectures held at a DMV Seminar in Blaubeuren by H.J. Baues, S. Halperin, and J.-M. Lemaire /
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| Imprint: | Basel ; Boston : Birkhäuser, 1995. |
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| Description: | ix, 117 p. : ill. ; 24 cm. |
| Language: | English |
| Series: | DMV Seminar. Bd. 24 |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/1740892 |
Table of Contents:
- Ch. 1. Basic Homotopy Theory. 1. Homotopy. 2. Cofibrations and fibrations
- Ch. 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
- Ch. 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
- Ch. 4. Algebraic Examples of Cofibration Categories. 1. The category CDA. 2. The category Chain+. 3. The category DA. 4. The category DL
- Ch. 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 Z/pZ. A.3. Sullivan Models
- Ch. 6. Attaching Cells in Topology and Algebra. 1. Algebraic models of spaces with a cell attached. 2. Inertia
- Ch. 7. Elliptic Spaces. 1. Finiteness of the formal dimension. 2. Elliptic models. 3. Some equalities and inequalities. 4. Topological interpretation
- Ch. 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
- Ch. 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.