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.

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