EVENT DETAILS AND ABSTRACT

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.