Index theory for elliptic operators invertible towards infinity

Hang Wang Íõº½  (ECNU)

10:00-11:00, June 9, 2020   Zoom 5146936752

Abstract:

An elliptic differential operator on a complete manifold, which is invertible outside a compact set, is Fredholm and also admits a higher index in the K-theory of the $C^*$-algebra of the fundamental group. Interesting examples involve manifolds admitting a positive scalar curvature metric outside a compact set and also the Atiyah-Patodi-Singer index theory for manifold with boundary (attaching a cylindrical end). We propose an approach to obtain the Fredholm index and its generalizations for this type of operators, as applications we obtain (equivariant) index formulas for manifolds with boundaries and with corners.