## EVENT DETAILS AND ABSTRACT

**Topology Seminar**
**Title:** Family Hirzebruch Signature Theorem with Converse

**Speaker:** Bruce Williams

**Speaker Info:** Notre Dame

**Brief Description:**

**Special Note**:

**Abstract:**

Let $X$ be a space which satisfies 4k-dim. Poincare Duality,
and let $\sigma(X)$ be the signature of $X$. If $X$ is a manifold, then $\sigma(X)$ can be ``disassembled'', i.e., $\sigma(X)$ is determined by a local invariant, the Hirzebruch $L$-polynomial. In this talk I'll give an enriched version of $\sigma(X)$ which is defined in all dimensions, and for dim >4, the enriched version can be disassembled if and only if $X$ admits a manifold structure. There is also a family version of this for fibrations.

**Date:** Wednesday, June 2, 2010

**Time:** 3:00pm

**Where:** Lunt 104

**Contact Person:** Prof. Paul Goerss

**Contact email:** pgoerss@math.northwestern.edu

**Contact Phone:** 847-491-8544

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