Event
Rapha毛l Ponge, Seoul National University
Cyclic homology, group actions and conformal invariants
In the first part of the talk, I will present some joint work with Hang Wang (U. Adelaide). We use 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 leads us to a construction of a whole new family of conformal invariants. The computation of these invariants uses the explicit computation of the cyclic homology of crossed-product algebras via explicit quasi-isomorphisms that I constructed recently. This computation will be the topic of the 2nd (and most important) part of the talk. This part involves a large amount of algebraic and differential topology. The results are expressed in terms of suitable versions of equivariant (co)homology in the sense of Borel and Bott. As a consequence this allows us to compute the conformal invariants of the 1st part in terms of equivariant characteristic classes.