# 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)

`P.Mitchener@sheffield.ac.uk`

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.