22 mar 2016 -- 15:00
Aula di Consiglio, Dip.Matematica, Università "La Sapienza", Roma
Abstract.
A pair of homotopy equivalent manifolds or a metric with positive scalar curvature on a Riemannian spin manifold give a vanishing analytic index (for the signature operator and the Dirac operator respectively). These situations produce secondary invariants (rho-classes) as lifting of K-homology classes to certain groups of K-theory. We define these invariants in the context of the Lipschitz manifolds and in the Lie groupoids setting, generalizing the Piazza-Schick construction in two different directions. Moreover we establish the cobordism invariance of the rho-classes (for suitable types of cobordisms). We also state a product formula that, under suitable conditions, gives stability results for the secondary invariants. Finally we will compare the Coarse and the Lie groupioids approach, establishing their equivalence.