# Diagram Cohomology and Isovariant Homotopy Theory

Share this page
*Giora Dula; Reinhard Schultz*

In algebraic topology, obstruction theory provides a way to study homotopy classes of continuous maps in terms of cohomology groups; a similar theory exists for certain spaces with group actions and maps that are compatible (that is, equivariant) with respect to the group actions. This work provides a corresponding setting for certain spaces with group actions and maps that are compatible in a stronger sense, called isovariant. The basic idea is to establish an equivalence between isovariant homotopy and equivariant homotopy for certain categories of diagrams. Consequences include isovariant versions of the usual Whitehead theorems for recognizing homotopy equivalences, an obstruction theory for deforming equivariant maps to isovariant maps, rational computations for the homotopy groups of certain spaces of isovariant functions, and applications to constructions and classification problems for differentiable group actions.

#### Table of Contents

# Table of Contents

## Diagram Cohomology and Isovariant Homotopy Theory

- Contents vii8 free
- Introduction 110 free
- 1. Equivariant homotopy in diagram categories 413 free
- 2. Quasistratifications 1221
- 3. Isovariant homotopy and maps of diagrams 1928
- 4. Almost isovariant maps 2736
- 5. Obstructions to isovariance 4049
- 6. Homotopy groups of isovariant function spaces 4857
- 7. Calculations with the spectral sequence 5564
- 8. Applications to differentiate group actions 6776
- Index of selected terms and symbols 7382 free
- References 7786