A mod 2 index theorem for pin− manifolds

Abstract

We establish a mod 2 index theorem for real vector bundles over 8k + 2 dimensional compact pin− manifolds. The analytic index is the reduced η invariant of (twisted) Dirac operators and the topological index is defined through KO-theory. Our main result extends the mod 2 index theorem of Atiyah and Singer (1971) to non-orientable manifolds.