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.
The talk is based on joint work with Nigel Higson.
About the speaker:
Zhizhang Xie is an assistant professor at Texas A&M University.
Attachments: