摘要
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.
We establish a mod 2 index theorem for real vector bundles over 8k ＋2 dimensional compact pinmanifolds. 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.
基金
supported by National Science Foundation of USA(Grant No.DMS 9022140)
through a Mathematical Sciences Research Institute(MSRI)postdoctoral fellowship
