Twisted Orbifold K-Theory
149 citations recorded by the source corpus.
Abstract: We use equivariant methods to define and study the orbifold K-theory of an orbifold X. Adapting techniques from equivariant K-theory, we construct a Chern character and exhibit a multiplicative decomposition for K*orb(X)⊗ℚ, in particular showing that it is additively isomorphic to the orbifold cohomology of X. A number of examples are provided. We then use the theory of projective representations to define the notion of twisted orbifold K–theory in the presence of discrete torsion. An explicit expression for this is obtained in the case of a global quotient.
Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/769fb4b4c7ca99267f1d1e2dae9aa3806e766422
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In Applied Mathematics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- On the $K$-theory of smooth toric DM stacks (2005, background): “orphism). Remark 5.5. If P Σ is projective, one can use the isomorphism of SRand orbifold cohomology to construct a map K 0(Σ,C) → H orb(P Σ,C). We suspect that this map is the Chern character map of [AR], which also motivated our terminology. But since our technique is quite different, we found it ”
- Surjectivity for Hamiltonian G-spaces in K-theory (2005, methodology): “Then the Kirwan map κ induced by the inclusion ι : If the G -action on the level set µ − 1 (0) is not free, then we take K ∗ ( M//G ) to be the orbifold K -theory, which for a global quotient is given, and in some cases defined, by [1] for further discussion of orbifold K -theory.”
- Asymptotic expansion of the heat kernel for orbifolds (2008, unknown): “See [1] for more details.”
- Orbifolds and Stringy Topology (2007, methodology): “We have the following theorem of Adem and Ruan [5].”