nLab Transformation Groups


This entry compiles material related to the textbook

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

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

See also:


Chapter I Foundations

  1. Basic notions

  2. General remarks. Examples

  3. Elementary properties

  4. Functorial properties

  5. Differentiable manifolds. Tubes and slices

  6. Families of subgroups

  7. Equivariant maps

  8. Bundles

  9. Vector bundles

  10. Orbit categories, fundamental groups, and coverings

  1. Elementary algebra of transformation groups

Chapter II Algebraic Topology

  1. Equivariant CW-complexes

  2. Maps between complexes

  3. Obstruction theory

  4. The classification theorem of Hopf

  5. Maps between complex representation spheres

  6. Stable homotopy. Homology. Cohomology

  7. Homology with families

  8. The Burnside ring and stable homotopy

  9. Bredon homology and Mackey functors

  10. Homotopy representations

Chapter III Localization

  1. Equivariant bundle cohomology

  2. Cohomology of some classifying spaces

  3. Localization

  4. Applications of localization

  5. Borel-Smith functions

  6. Further results for cyclic groups. Applications

Chapter IV The Burnside Ring

  1. Additive invariants

  2. The Burnside ring

  3. The space of subgroups

  4. Prime ideals

  5. Congruences

  6. Finiteness theorems

  7. Idempotent elements

  8. Induction categories

  9. Induction theory

  10. The Burnside ring and localization

category: reference

Last revised on December 28, 2021 at 14:18:14. See the history of this page for a list of all contributions to it.