Dehn functions of solvable Lie groupsMPIM

by Gabriel Pallier (University of Lille)

Thursday Apr 16, 2026, 1:30 PM → 2:30 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

Oberseminar Differentialgeometrie 

In the seventees, Herbert Abels studied the compact presentability of solvable groups in order to establish criteria for finite presentability of certain S-arithmetic groups. In the 2010s Cornulier and Tessera revived Abel's theorems in a more quantitative way: they gave an algorithmic deciding whether the Dehn functions of solvable Lie groups is exponential or polynomially bounded. We will be interested in an even more precise question: in the case when the Dehn function is polynomially bounded, what is its polynomial order? Making Cornulier-Tessera's theorems more explicit, we will see that it is estimated by that of the largest nilpotent quotient. Finally we will show how Cornulier and Tessera's bound can be improved on the example of a central product of Abel's second group and a filiform group of class three.