Twisted K-theory and loop groups

TL;DR

This paper explores models of twisted K-theory and establishes a connection between loop group representations and twisted equivariant K-theory, contributing to both mathematical theory and physical applications.

Contribution

It introduces models of twisted K-theory and proves a theorem linking loop group representations to twisted equivariant K-theory, advancing understanding in both fields.

Findings

Models of twisted K-theory developed

Theorem relating loop group representations to twisted K-theory proved

Enhanced understanding of twisted K-theory's applications in physics

Abstract

Twisted K-theory has received much attention recently in both mathematics and physics. We describe some models of twisted K-theory, both topological and geometric. Then we state a theorem which relates representations of loop groups to twisted equivariant K-theory. This is joint work with Michael Hopkins and Constantin Teleman.