Geometric Analysis and Topology Seminar

---

Extending Poincare Duality to Homotopically Stratified Spaces

Speaker: Greg Friedman, Vanderbilt

Location: Warren Weaver Hall 813

Date: Friday, April 28, 2006, 2 p.m.

Synopsis:

In the early 1980s, Goresky and MacPherson introduced intersection homology in order to extend a version of Poincare Duality to certain non-manifold spaces, in particular spaces such as algebraic varieties that are composed of manifold strata of various dimensions. These spaces also require strict local conditions by which all points must have product neighborhoods of a certain form. Quinn later introduced the notion of a Manifold Homotopically Stratified Space, which is also composed of manifold strata but for which the local neighborhood data has been replaced by homotopy conditions. These spaces were intended to "give a setting for the study of purely topological stratified phenomena," and the homotopy properties were considered "more appropriate for the study of a homology theory." By employing the singular intersection chains of King and results of Hughes on approximate tubular neighborhoods, we show that the Goresky-MacPherson extension of Poincare Duality using intersection homology applies as well to Quinn's spaces.