Speaker:  Prof. John Klein, WSU

Title: Poincaré complex diagonals and the Bass trace conjecture

Abstract:  Let M be a manifold. Then M has a tangent bundle, or equivalently,  the diagonal M -> M x M has a tubular neighborhood.

However, for Poincaré duality spaces, the analog of this statement is not known in general. The goal of this talk is to explain what this means and to give the total obstruction to solving the problem of finding a "Poincaré tubular neighborhood" of the diagonal.

I will explain how a symmetrization of the obstruction vanishes for Poincaré duality spaces that have the homotopy type of a finite complex.

I will also explain how this problem relates to an old conjecture of Hyman Bass on the Hattori-Stallings trace map.

This is joint work with Florian Naef.