group cohomology, nonabelian group cohomology, Lie group cohomology
Hochschild cohomology, cyclic cohomology?
cohomology with constant coefficients / with a local system of coefficients
differential cohomology
geometric representation theory
representation, 2-representation, ∞-representation
Grothendieck group, lambda-ring, symmetric function, formal group
principal bundle, torsor, vector bundle, Atiyah Lie algebroid
Eilenberg-Moore category, algebra over an operad, actegory, crossed module
Be?linson-Bernstein localization?
and
rational homotopy theory (equivariant, stable, parametrized, equivariant & stable, parametrized & stable)
Examples of Sullivan models in rational homotopy theory:
The equivariant Chern-Dold character is the generalization of the Chern-Dold character from Whitehead-generalized cohomology to equivariant cohomology, and the generalization of the equivariant Chern character on equivariant K-theory to other equivariant generalized cohomology theories.
Wolfgang Lück, Chern characters for proper equivariant homology theories and applications to K- and L-theory, Journal für die reine und angewandte Mathematik, Volume 2002: Issue 543 (doi:10.1515/crll.2002.015, pdf)
Wolfgang Lück, Equivariant Cohomological Chern Characters, International Journal of Algebra and ComputationVol. 15, No. 05n06, pp. 1025-1052 (2005) (arXiv:math/0401047, doi:10.1142/S0218196705002773)
Wolfgang Lück, Equivariant Chern characters, 2006 (pdf, pdf)
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