Noncommutative Geometry Seminar

Date: October 14, 2020

Time: 1:00PM - 2:00PM

Location: Zoom 942810031

Speaker: Paolo Piazza, Università di Roma La Sapienza

Title: Higher genera and C*-indices on G-proper manifolds

Abstract: Higher general for a G-proper manifold without boundary can be defined in analogy with Galois coverings and they are, by definition, geometric objects. To understand their stability properties we need to connect them to higher C^*-indices of suitable Dirac operators. This is possible but under additional assumptions on the group G, for example G semisimple and connected and more generally G satisfying the Rapid Decay condition and G/K of nonpositive sectional curvature. I will begin my talk by explaining these results. I will then move to manifolds with boundary and explain how it is possible to define higher genera in this more complicated situation. Crucial to the analysis is a higher C^*-index theorem of Atiyah-Patodi-Singer type. All these results, the last very recent, are in collaboration with Hessel Posthuma.

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