Filling functions for finite presentations of groups
by
Tim Riley
Yale
Coauthors: M.R.Bridson, S.M.Gersten

The Cayley 2-complex is a simply connected space associated to a finite presentation of a group. Filling functions capture aspects of the geometry of "filling" discs spanning loops in this space, and are important group invariants. Many natural questions arise about the interrelationships between filling functions. For example, one might ask: given knowledge about the areas of fillings, what can be said about their diameters? I will survey work, undertaken in collaborations with Martin Bridson and Steve Gersten, on such questions.

Date received: September 16, 2004