Geometric presentations of Lie groups and their Dehn functions

Yves Cornulier; Romain Tessera

doi:10.1007/s10240-016-0087-3

Yves Cornulier ¹ ; Romain Tessera ¹

¹Laboratoire de Mathématiques, Bâtiment 425, Université Paris-Sud 11 91405 Orsay France

Publications Mathématiques de l'IHÉS, Volume 125 (2017), pp. 79-219

Abstract

We study the Dehn function of connected Lie groups. We show that this function is always exponential or polynomially bounded, according to the geometry of weights and of the 2-cohomology of their Lie algebras. Our work, which also addresses algebraic groups over local fields, uses and extends Abels’ theory of multiamalgams of graded Lie algebras, in order to provide workable presentations of these groups.

Received: 2013-11-01
Accepted: 2016-11-28
Online First: 2016-12-20
Published online: 2017-06-07

MR Zbl

DOI: 10.1007/s10240-016-0087-3

Author's affiliations:

Yves Cornulier ¹ ; Romain Tessera ¹

¹ Laboratoire de Mathématiques, Bâtiment 425, Université Paris-Sud 11 91405 Orsay France

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     title = {Geometric presentations of {Lie} groups and their {Dehn} functions},
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Yves Cornulier; Romain Tessera. Geometric presentations of Lie groups and their Dehn functions. Publications Mathématiques de l'IHÉS, Volume 125 (2017), pp. 79-219. doi: 10.1007/s10240-016-0087-3

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