Higher signatures on Witt spaces

Zhizhang Xie  (Texas A&M University)

14:00 pm to 14:50 pm, June 2nd, 2015   Science Building A1414

Abstract:

The signature is a fundamental homotopy invariant for topological manifolds. However, for spaces with singularities, this usual notion of signa- ture ceases to exist, since, in general, spaces with singularities fail the usual Poincare duality. A generalized Poincare duality theorem for spaces with singularities was proven by Goresky and MacPherson using intersection homology. The classical signature was then extended to Witt spaces by Siegel using this generalized Poincare duality. Witt spaces are a natural class of spaces with singularities. For example, all complex algebraic varieties are Witt spaces. In this talk, I will describe a combinatorial approach to higher signatures of Witt spaces, using methods of noncommutative geometry.

The talk is based on joint work with Nigel Higson.