Density of isoperimetric spectra

Geometry Topology Seminar
Monday, April 6, 2009 - 16:00
1 hour (actually 50 minutes)
Emory, W306 MSC (Math and Science Center)
University of Oklahoma

Joint meeting at Emory

A k--dimensional Dehn function of a group gives bounds on the volumes of (k+1)-balls which fill k--spheres in a geometric model for the group. For example, the 1-dimensional Dehn function of the group Z^2 is quadratic. This corresponds to the fact that loops in the euclidean plane R^2 (which is a geometric model for Z^2) have quadratic area disk fillings. In this talk we will consider the countable sets IP^{(k)} of numbers a for which x^a is a k-dimensional Dehn function of some group. The situation k \geq 2 is very different from the case k=1.