# Algebraic Topology

### What shape' is space-time?

#### Summary:

Some examples from the mathematics of shape are presented that question some of the almost hidden assumptions behind results on limiting behaviour of finitary approximations to space-time. These are presented so as to focus attention on the observational problem of refinement and suggest the necessity for an alternative theory of fractafolds' against which the limiting theory of C^\infty-differential manifolds usually underlying (quantum) general relativity can be measured.

### Groupoid atlases: an introduction

#### Summary:

Abstract of talk to the 'Colloque International: Charles Ehresmann: 100ans', Amiens 7-9 October, 2005.