Jerónimo García-Mejía (Karlsruhe Institute of Technology) : Dehn functions of (central products of) nilpotent groups

Séminaires Séminaire « Géométrie dynamique » math
Salle Visio M3

Since the celebrated Gromov's polynomial growth theorem, the study of nilpotent groups has emerged as a central theme in geometric group theory. A particularly interesting aspect is the conjectural quasiisometry classification of nilpotent groups. An important quasiisometry invariant for a finitely presented group is its Dehn function. This function provides a quantitative measure to detect if a word in the generating set represents the identity element in the group. 

Thanks to the work of Gersten, Holt and Riley we now understand that the Dehn function of a nilpotent group of class c is bounded above by nc+1. In this talk,  I will explain recent results that allow us to determine the Dehn functions of large classes of nilpotent groups. As a consequence we obtain a large collection of pairs of nilpotent groups with bilipschitz equivalent asymptotic cones but with different Dehn functions.

This talk is based on joint work with Claudio Llosa Isenrich and Gabriel Pallier.

Lamination géodésique. Adam Majewski, CC BY-SA 3.0

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