equivariant rational homotopy theory



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



Paths and cylinders

Homotopy groups

Basic facts


Representation theory

Rational homotopy theory



The equivariant version of rational homotopy theory.


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, ISBN: 978-0-8218-0319-6)

  • Georgia Triantafillou, Equivariant minimal models, Trans. Amer. Math. Soc. vol 274 pp 509-532 (1982) (jstor:1999119)

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

Further discussion in:

The model structure on equivariant dgc-algebras, generalizing the projective model structure on dgc-algebras, in which equivariant minimal Sullivan models are cofibrant objects:

See also

  • Peter J. Kahn, Rational Moore G-Spaces, Transactions of the American Mathematical Society Vol. 298, No. 1 (1986), pp. 245-271 (jstor:2000619)

  • 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 October 24, 2020 at 10:00:55. See the history of this page for a list of all contributions to it.