Scaled relators and Dehn functions for nilpotent groups
by
Robert Young
University of Chicago

A homogeneous nilpotent Lie group has a scaling automorphism determined by a grading of its Lie algebra. Many proofs of upper bounds for the Dehn function of such a group depend on being able to fill curves with discs compatible with this grading; the area of such discs changes predictably under the scaling automorphism. We will present combinatorial methods for finding such bounds. Applications include constructing the first example of a torsion-free nilpotent group of class 3 with a quadratic Dehn function.

Date received: February 21, 2006