nLab Transformation Groups and Representation Theory

This page compiles material related to the textbook:

• Tammo tom Dieck,

  Transformation Groups and Representation Theory

  Lecture Notes in Mathematics 766

  Springer 1979

  (doi:10.1007/BFb0085965)

on transformation groups/topological G-spaces, representation theory, equivariant homotopy theory, equivariant cohomology.

Beware the existence of a book of similar title, by the same author and largely on the same subjects:

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

See also

• Glen Bredon, Introduction to compact transformation groups, Academic Press 1972 (ISBN 9780080873596

  , pdf)

front matter

Chapter 1: The Burnside ring of finite G-sets

• G-set

• Burnside ring

Chapter 3: Lambda rings

• lambda ring

• Adams operation

Chapter 4: Permutation representations

• permutation representation

Chapter 5: The Burnside ring of a compact Lie group

Chapter 7: Equivariant homology and cohomolgy

• equivariant cohomology

• Bredon equivariant cohomology

• equivariant Adams conjecture

Chapter 8: Equivariant homotopy theory

• G-space

• equivariant homotopy theory

• equivariant Hopf degree theorem

• equivariant stable cohomotopy

• Burnside ring is equivariant stable cohomotopy of the point

Chapter 10: Geometric modules over the Burnside ring

Chapter 11: Homotopy equivalent stable G-vector bundles

• J-homomorphism

References

category: reference