Freed-Moore K-theory
Abstract
The twisted equivariant K-theory given by Freed and Moore is a K-theory which unifies twisted equivariant complex K-theory, Atiyah's `Real' K-theory, and their variants. In a general setting, we formulate this K-theory by using Fredholm operators, and establish basic properties such as the Bott periodicity and the Thom isomorphism. We also provide formulations of the K-theory based on Karoubi's gradations in both infinite and finite dimensions, clarifying their relationship with the Fredholm formulation.
- Publication:
-
arXiv e-prints
- Pub Date:
- May 2017
- DOI:
- 10.48550/arXiv.1705.09134
- arXiv:
- arXiv:1705.09134
- Bibcode:
- 2017arXiv170509134G
- Keywords:
-
- Mathematics - K-Theory and Homology;
- 19L50
- E-Print:
- 61 pages, LaTeX 2e