Manchester Geometry Seminar 2008/2009

Thursday 27 November 2008. The Frank Adams Room (Room 1.212), the Alan Turing Building. 4pm

Coarse Geometry, Cell Complexes, and Connections with Positive Scalar Curvature

Paul Mitchener (University of Sheffield)

We describe the coarse category, and look at the coarse version of a homology theory. We then look at an isomorphism conjecture for coarse homology theories, called the coarse Baum-Connes conjecture, and prove it for finite-dimensional coarse cellular complexes; another concept we shall describe in the talk.

To conclude, we formulate the Gromov-Lawson conjecture on the existence of positive scalar curvature metrics on certain manifolds, and indicate how the coarse Baum-Connes conjecture implies it.

The talk is intended to be elementary, and suitable for a general mathematical audience with interest in geometry and topology.