# Geometric Analysis and Topology Seminar

#### Smooth Deformation of Singularities and Generalized Poincare Complexes: A Stability Theorem and a de Rham Theorem

**Speaker:**
Markus Banagl, Heidelberg

**Location:**
Warren Weaver Hall 202

**Date:**
Friday, October 15, 2010, 11 a.m.

**Synopsis:**

In many situations, it is homotopy theoretically possible to associate to a singular space in a natural way a generalized geometric Poincare complex, whose cohomology turns out to be a new cohomology theory for singular spaces, not isomorphic in general to intersection cohomology or L2-cohomology. Using vertically harmonic differential forms, we provide a de Rham type description of the new theory. While intersection cohomology is stable under small resolutions, the new theory is often stable under deformations of singularities. The latter result is partly joint work with Laurentiu Maxim.