Twisted K Theory Invariants

An invariant for twisted K theory classes on a 3-manifold is introduced. The invariant is then applied to the twisted equivariant classes arising from the supersymmetric Wess–Zumino–Witten model based on the group SU(2). It is shown that the classes defined by different highest weight representations of the loop group LSU(2) are inequivalent. The results are compatible with Freed–Hopkins–Teleman identification of twisted equivariant K theory as the Verlinde algebra.