Title: Index theory for elliptic operators invertible at infinity
Speaker: Hang Wang (East China Normal University)
Time: 16:00-17:00, July15
Location: Tecent Meeting, Tecent Meeting ID: 338 396 016, Password: 654321
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. This is joint work with Peter Hochs and Bai-Ling Wang and with Xiaoman Chen, Hongzhi Liu and Guoliang Yu.
Video Link: https://www.bilibili.com/video/BV11A411e7Xx/
