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 $n$-types

5 Cohomology of groups and cohomology of categories

6 Simply connectd homotopy types and $H\pi$-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

References

Linked Reference:

• Handbook of Algebraic Topology, ed. I. M.James, Elsevier Science, 1995.

category: reference