Geometric presentations of Lie groups and their Dehn functions

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.Comment: 137 pages, a few figures. v1->v2: the paper has been thoroughly reorganized in order to be more readable. The numbering of theorems is therefore modifie

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