nLab Introduction to compact transformation groups

This entry colllects material related to the book

• Glen Bredon,

  Introduction to compact transformation groups

  Academic Press 1972

  ISBN 9780080873596

  pdf

on transformation groups/topological G-spaces and their equivariant differential topology, equivariant homotopy theory and equivariant cohomology (Bredon cohomology).

See also

• Tammo tom Dieck, Transformation Groups and Representation Theory, Lecture Notes in Mathematics 766, Springer 1979 (doi:10.1007/BFb0085965)

• Tammo tom Dieck, Transformation Groups, de Gruyter 1987 (doi:10.1515/9783110858372)

0 Background on Topological Groups and Lie Groups

1. Elementary properties of topological groups

• topological group

• normalizer subgroup

2. The classical groups

• classical Lie group

3. Integration on compact groups

• Haar measure

4. Characteristic functions on compact groups

5. Lie groups

• Lie group

6. The structure of compact Lie groups

• compact Lie group

I Transformation Groups

• group action, topological G-space

• equivariant function

• isotropy group

• orbit

• homogeneous space, coset space, orbit type

• slice theorem

• fixed points

II General Theory of $G$-Spaces

1. Fiber bundles

• fiber bundle

2. Associated bundles

• associated bundle

• slice theorem

3. Twisted products with a compact group

4. Tubes and slices

III Homological Theory of Finite Group Actions

IV Locally Smooth Actions on Manifolds

V Actions with Few Orbit Types

VI Smooth Actions

• equivariant tubular neighbourhood

• invariant Riemannian metric

Chapter VII Cohomology Structure of Fixed Point Sets

category: reference