| Résume | The Dehn function of a finitely presented group provides a quantitative measure for the difficulty of detecting if a word in its generators represents the trivial element of the group. By work of Gersten, Holt and Riley the Dehn function of a nilpotent group of class c is bounded above by n^{c+1}. However, we are still far from determining the precise Dehn functions of all nilpotent groups. Since Dehn functions are quasi-isometry invariants, progress on this problem may lead to insights to the quasi-isometry classification of nilpotent groups. I will explain recent results that allow us to determine the precise Dehn functions of many nilpotent groups arising as central products. I will also present some consequences of these results, such as the existence of a pair of finitely presented groups with the same asymptotic cone, but with different Dehn functions. This talk is based on joint works with Pallier and Tessera, and with García-Mejía and Pallier. |
