nLab Homotopy Types

This page compiles pointers related to:

• Hans Baues:

  
  

  Homotopy Types

  pdf, pdf

  
  

  in:

  Ioan M. James (ed):

  Handbook of Algebraic Topology

  Oxford 1995

  ISBN:9780080532981

  doi:10.1016/B978-0-444-81779-2.X5000-7

on homotopy theory with focus on the notion of homotopy types.

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).

What are homotopy types?

How to build homotopy types

Whitehead’s realization problem

Algebraic models of $n$-types

Cohomology of groups and cohomology of categories

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

The Hurewicz homomorphism

Postnikov invariants and boundary invariants

The classification theorems

Stable homotopy types

Decomposition of stable homotopy types

Localization

References

category: reference