Introduction to compact transformation groups in nLab

This page is to record the reference:

* [[Glen Bredon]], 

  **Introduction to compact transformation groups** 

  Pure and Applied Mathematics **46**

  Academic Press (1972)

  [ISBN:978-0-12-128850-1](https://www.sciencedirect.com/bookseries/pure-and-applied-mathematics/vol/46)

  [ISBN 9780080873596](https://www.elsevier.com/books/introduction-to-compact-transformation-groups/bredon/978-0-12-128850-1)


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](https://link.springer.com/book/10.1007/BFb0085965))

* [[Tammo tom Dieck]], _[[Transformation Groups]]_, de Gruyter 1987  ([doi:10.1515/9783110858372]( https://doi.org/10.1515/9783110858372))



#Contents#
* table of contents
{:toc}


## 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