Geometric K-homology and the Freed-Hopkins-Teleman theorem

2018/04/14 by Loizides, Yiannis
#FOS: Mathematics #K-Theory and Homology (math.KT) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1804.05213

Abstract

We describe a map from the equivariant twisted K-homology of a compact, connected, simply connected Lie group G to the Verlinde ring. Our map is described at the level of `D-cycles' for the geometric twisted K-homology of G, and is inverse to the Freed-Hopkins-Teleman isomorphism. As an application, we show that two possible definitions of the `quantization' of a Hamiltonian loop group space are compatible with each other.

Related

• Verlinde modules and quantization
• Twisted K-theory and loop group representations
• Completing Verlinde Algebras
• Loop Groups and Twisted K-Theory II
• Naturality of FHT isomorphism