Veranstaltung

Vortrag
Rho invariants in topology and differential geometry
Paolo Piazza
1.11.2007, 16:00 Uhr – 16:50 Uhr

Rho-invariants are secondary invariants of Dirac operators; the aim of this talk is to survey the basic results in the field, explain their interest and announce a few recent results about their generalization to the foliated context. More precisely, let G be a discrete group and let M be a closed oriented manifold with fundamental group G. I will consider various rho-invariants associated to the signature operator on M and to the Dirac operator (in the spin case) : the Atiyah-Patodi-Singer rho invariant, the Cheeger-Gromov rho-invariant and the delocalized rho-invariant of Lott. I will talk about the behavior of these rho-invariants under deformation of the metric, or of the differentiable structure or of the homotopy type of the manifold: rather surprisingly, this behavior depends on the nature of the fundamental group of the manifold and is radically different depending whether the group G has torsion or is torsion-free. In the last part of my talk I will move to measured foliations and announce recent results in collaboration with Moulay Benameur.

Verknüpft mit:

• Paolo Piazza