nLab 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, dealing with rationalization in (proper) equivariant homotopy theory, detected by Bredon equivariant rational cohomology.


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. 274 (1982) 509-532 [jstor:1999119]

but beware that Scull 01 claims that the statement about minimal models there is not correct. Corrected 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:

partially reviewed also in

  • Rekha Santhanam, Soumyadip Thandar, §2 of: Equivariant Intrinsic Formality [arXiv:2301.06824]

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 May 10, 2024 at 13:42:06. See the history of this page for a list of all contributions to it.