nLab
equivariant rational homotopy theory

Contents

Context

Homotopy theory

homotopy theory, (∞,1)-category theory, homotopy type theory

flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed

models: topological, simplicial, localic, …

see also algebraic topology

Introductions

Definitions

Paths and cylinders

Homotopy groups

Basic facts

Theorems

Representation theory

Rational homotopy theory

Contents

Idea

The equivariant version of rational homotopy theory.

References

The original reference for finite groups is

  • Georgia Triantafillou, Equivariant rational homotopy theory, chapter III of Peter May, Equivariant homotopy and cohomology theory CBMS Regional Conference Series in Mathematics, vol. 91, Published for the Conference Board of the Mathematical Sciences, Washington, DC, 1996. With contributions by M. Cole, G. Comeza˜na, S. Costenoble, A. D. Elmendorf, J. P. C. Greenlees, L. G. Lewis, Jr., R. J. Piacenza, G. Triantafillou, and S. Waner. (pdf)

  • Georgia Triantafillou, Equivariant minimal models, Trans. Amer. Math. Soc. vol 274 pp 509-532 (1982) (jstor)

but beware that Scull 01 claims that the statement about minimal models there is not correct. Corrrected statements for finite groups as well as generalization to compact Lie groups, at least to the circle group, is due to

  • Laura Scull, Rational S 1S^1-equivariant homotopy theory, Transactions of the AMS, Volume 354, Number 1, Pages 1-45 2001 (pdf)

See also

  • C. Allday, V. Puppe, sections 3.3 and 3.4 of Cohomological methods in transformation groups, Cambridge 1993 (doi:10.1017/CBO9780511526275)

Last revised on February 6, 2019 at 05:11:25. See the history of this page for a list of all contributions to it.