Nilpotent groups without exactly polynomial Dehn function

2010/04/16 by Stefan Wenger, Wenger, Stefan
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Group Theory (math.GR) #math.DG #math.GR

paper · pdf · doi:10.48550/arxiv.1004.2907

arxiv created 2010/04/16 · arxiv updated 2010/04/19

Abstract

We prove super-quadratic lower bounds for the growth of the filling area function of a certain class of Carnot 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.

Related

• Filling inequalities for nilpotent groups
• Polynomially-bounded Dehn functions of groups
• Scaled relators and Dehn functions for nilpotent groups
• Groups with quadratic-non-quadratic Dehn functions
• Finitely presented simple groups with at least exponential Dehn function