Orientations in K-theory: Thom and Fundamental Classes

13.06.2025 14:00 – 15:00

We present the notion of orientations and orientability of smooth manifolds and vector bundles in K-theory and show using Clifford modules that being Spin^c and even dimensional is a necessary and sufficient condition to be K-orientable. We then go on to show that the canonical Dirac operator of such manifolds represents the fundamental class by inducing Poincaré duality isomorphisms, by explaining why its symbol is the Thom class of the cotangent bundle of the manifold.

Lieu

Conseil Général 7-9, Room 1-07,

entrée libre