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Geometric presentations of Lie groups and their Dehn functions

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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.

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Authors and Affiliations

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

    Yves Cornulier & Romain Tessera

Authors
  1. Yves Cornulier
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  2. Romain Tessera
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Corresponding author

Correspondence to Yves Cornulier.

Additional information

The authors are supported by ANR Project GAMME (ANR-14-CE25-0004).

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Cornulier, Y., Tessera, R. Geometric presentations of Lie groups and their Dehn functions. Publ.math.IHES 125, 79–219 (2017). https://doi.org/10.1007/s10240-016-0087-3

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