Noncommutative Geometry, Conformal Geometry, and Cyclic Homology of Group Actions on Manifolds
Raphael Ponge (Seoul National University)
Tuesday 10th January, 2017 16:00-17:00 Maths 522
In this talk I will explain how to apply tools of noncommutative geometry to obtain a local index formula in conformal geometry that takes into account the action of an arbitrary group of conformal diffeomorphisms. This uses the framework of twisted spectral triples of Connes-Moscovici. This leads us to a construction of a whole new family of conformal invariants. These invariants are expressed in terms of equivariant characteristic classes. Their computation was an important impetus for the explicit calculation of the cyclic homology of crossed-product algebras associated with group actions on manifolds. This solves an important problem in noncommutative geometry.