group cohomology, nonabelian group cohomology, Lie group 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 character is the generalization of the Chern character from topological K-theory to equivariant topological K-theory, equivalently the specialization of the equivariant Chern-Dold character for generalized equivariant cohomology to equivariant topological K-theory.
The equivariant Chern character has a variety of different but equivalent concrete incarnations, depending on the choice of presentation of the rational equivariant K-theory that it takes values in:
Incarnations of rational equivariant K-theory:
Jolanta Słomińska, On the Equivariant Chern homomorphism, Bull. Acad. Polon. Sci., Sér. Sci. Math. Astronom. Phys, Vol. 24 (1976), 909-913.
Alain Connes, Paul Baum, Chern character for discrete groups, A Fête of Topology, Papers Dedicated to Itiro Tamura 1988, Pages 163-232 (doi:10.1016/B978-0-12-480440-1.50015-0)
Michel Duflo, Michèle Vergne, Cohomologie équivariante et descente, Astérisque, no. 215 (1993) (numdam:AST_1993__215__5_0)
Wolfgang Lück, Bob Oliver, Chern characters for the equivariant K-theory of proper G-CW-complexes, In: Aguadé J., Broto C., Casacuberta C. (eds.) Cohomological Methods in Homotopy Theory, Progress in Mathematics, vol 196. Birkhäuser 2001 (doi:10.1007/978-3-0348-8312-2_15, pdf)
Alejandro Adem, Yongbin Ruan, Section 5 of: Twisted Orbifold K-Theory, Commun. Math. Phys. 237 (2003) 533-556 (arXiv:math/0107168)
Varghese Mathai, Danny Stevenson, Chern character in twisted K-theory: equivariant and holomorphic cases, Commun. Math. Phys. 236 161-186, 2003 (arXiv:hep-th/0201010, doi:10.1007/s00220-003-0807-7)
Ieke Moerdijk, p. 18 of: Orbifolds as Groupoids: an Introduction, in: Alejandro Adem, Jack Morava, Yongbin Ruan (eds.) Orbifolds in Mathematics and Physics, Contemporary Math 310 , AMS (2002), 205–222 (arXiv:math.DG/0203100)
Guido Mislin, Alain Valette, Theorem 6.1 in: Proper Group Actions and the Baum-Connes Conjecture, Advanced Courses in Mathematics CRM Barcelona, Springer 2003 (doi:10.1007/978-3-0348-8089-3)
Ulrich Bunke, Markus Spitzweck, Thomas Schick, Inertia and delocalized twisted cohomology, Homotopy, Homology and Applications, vol 10(1), pp 129-180 (2008) (arXiv:math/0609576, doi:10.4310/HHA.2008.v10.n1.a6)
Pierre Albin, Richard Melrose, Delocalized equivariant cohomology and resolution (arXiv:1012.5766)
Review in:
Ulrich Bunke, Section 3.1 in: Orbifold index and equivariant K-homology, Math. Ann. 339, 175–194 (2007) (arXiv:math/0701768, doi:10.1007/s00208-007-0111-5)
German Stefanich, Chern Character in Twisted and Equivariant K-Theory (pdf)
Last revised on December 20, 2021 at 10:14:47. See the history of this page for a list of all contributions to it.