An L2-Index Theorem for Dirac Operators on S1×R3

An expression is found for the L2-index of a Dirac operator coupled to a connection on a Un vector bundle over S1×R3. Boundary conditions for the connection are given which ensure the coupled Dirac operator Fredholm. Calliasʹ index theorem is used to calculate the index when the connection is independent of the coordinate on S1. An excision theorem due to Gromov, Lawson, and Anghel reduces the index theorem to this special case.