Freed-Moore K-theory

Understand

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.