Nilpotent groups without exactly polynomial Dehn function

Abstract

We prove super-quadratic lower bounds for the growth of the filling area function of a certain class of nilpotent Lie groups. This class contains groups for which it is known that their Dehn function grows no faster than n2log n. We therefore obtain the existence of (finitely generated) nilpotent groups whose Dehn functions do not have exactly polynomial growth and we thus answer a well-known question about the possible growth rate of Dehn functions of nilpotent groups.