Author(s): Biedermann, Georg; Raptis, Georgios; Stelzer, Manfred
Series: Astérisque 393
Publisher: SMF
Year: 2017
Language: English
Pages: 148
Tags: Algebraic topology
Chapter 1. Introduction
Chapter 2. Resolution model categories
2.1. Cosimplicial objects
2.2. Cosimplicial resolutions
2.3. G-cofree and quasi-G-cofree maps
Chapter 3. Natural homotopy groups
3.1. Basic properties of the natural homotopy groups
3.2. Algebraic structures on homotopy groups
3.3. The spiral exact sequence
3.4. Cosimplicial connectivity
Chapter 4. Cosimplicial unstable coalgebras
4.1. Preliminaries
4.2. Homology and F-GEMs
4.3. Cosimplicial resolutions of unstable coalgebras
4.4. Cosimplicial comodules over a cosimplicial coalgebra
4.5. Spectral sequences
4.6. Homotopy excision
Chapter 5. André-Quillen cohomology
5.1. Coabelian objects
5.2. André-Quillen cohomology
5.3. Objects of type KC(M,n)
5.4. Postnikov decompositions
5.5. An extension of Proposition 5.4.1
Chapter 6. Cosimplicial spaces
6.1. Cosimplicial resolutions of spaces
6.2. Consequences of the Künneth theorem
6.3. Objects of type LC(M,n)
6.4. Postnikov decompositions
Chapter 7. Moduli spaces of topological realizations
7.1. Potential n-stages
7.2. The main results
7.3. Moduli spaces of marked topological realizations
7.4. Obstruction theories
Appendix A. The spiral exact sequence
A.1. Constructing the exact sequence
A.2. The spiral exact sequence and 0-modules
A.3. The spiral spectral sequence
Appendix B. Hun-algebras and unstable algebras
B.1. The cohomology of Eilenberg-MacLane spaces
B.2. Algebraic theories
B.3. Unstable algebras are Hun-algebras
B.4. Unstable algebras, rationally
B.5. The cohomology spectral sequence
Appendix C. Moduli spaces in homotopy theory
C.1. Simplicial localization
C.2. Models for mapping spaces
C.3. Moduli spaces
C.4. A moduli space associated with a directed diagram
Bibliography
