Appears in collection : 2025 - T1 - WS1 - Intertwining operators and geometry

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. This is joint work with Paulo Carrillo Rouse and Zijing Wang.