nLab
equivariant Chern character

Idea

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.

Related concepts

• twisted Chern character

• equivariant Chern-Dold character

• equivariant rationalization

• delocalized equivariant cohomology

• Chen-Ruan cohomology

References

• 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)

• 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)

• 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)

• 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)