nLab Homotopy Types

Homotopy Types

This 72 page article, by Hans Baues, is to be found in the Handbook of Algebraic Topology. It starts from a basic position and attacks three main topics:

  • Homotopy types with non-trivial fundamental group (Sections 2 - 5);

  • Homotopy types with trivial fundamental group (Sections 6 - 9, 12);

  • Stable homotopy types (Sections 10 and 11).


1 What are homotopy types?

2 How to build homotopy types

3 Whitehead’s realization problem

4 Algebraic models of nn-types

5 Cohomology of groups and cohomology of categories

6 Simply connectd homotopy types and HπH\pi-duality

7 The Hurewicz homomorphism

8 Postnikov invariants and boundary invariants

9 The classification theorems

10 Stable homotopy types

11 Decomposition of stable homotopy types

12 Localization


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Last revised on September 10, 2012 at 20:38:26. See the history of this page for a list of all contributions to it.