More about cobordisms and weak complicial sets

Dominic Verity – 23 July 2008

A few months ago we embarked on a journey to discover how certain kinds of simplicial weak omega-categories (weak complicial sets) could be built to support the algebra of cobordisms. At that time, the activities of the semester interrupted these ruminations. In this talk (and the next) we return to this topic, review the fundamental constructions involved and push on to study the kinds of equivalence that arise in such structures. This latter analysis reveals a family of nested thinness notions (stratifications) each one of which makes the simplicial set of cobordisms into a weak complicial set.