AG Lie-Gruppen: H. Wang, East China Normal University: Cohomological Insights into the Connes-Kasparov Isomorphism

Cohomological Insights into the Connes-Kasparov Isomorphism – Vortragende: Hang Wang, East China Normal University – Einladender: Kang Li

Abstract: A Riemann-Roch type formula serves as the the cornerstone in establishing the
Atiyah-Singer index theory via the K-theory method. The classical
deformation-to-the-normal-cone approach offers a perspective from noncommutative
geometry on formulating the analytic index. In this work, we propose a
topological method that combines a Riemann-Roch theorem with
deformation-to-the-normal-cone techniques to provide a cohomological depiction
of the Connes-Kasparov isomorphism. We anticipate that this framework will
yield all local index formulas. This is joint work with Paulo Carrillo Rouse.