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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.
@article{PMIHES_2017__125__79_0,
author = {Cornulier, Yves and Tessera, Romain},
title = {Geometric presentations of {Lie} groups and their {Dehn} functions},
journal = {Publications Math\'ematiques de l'IH\'ES},
pages = {79--219},
publisher = {Springer Berlin Heidelberg},
address = {Berlin/Heidelberg},
volume = {125},
year = {2017},
doi = {10.1007/s10240-016-0087-3},
mrnumber = {3668649},
zbl = {1428.22012},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1007/s10240-016-0087-3/}
}
TY - JOUR AU - Cornulier, Yves AU - Tessera, Romain TI - Geometric presentations of Lie groups and their Dehn functions JO - Publications Mathématiques de l'IHÉS PY - 2017 SP - 79 EP - 219 VL - 125 PB - Springer Berlin Heidelberg PP - Berlin/Heidelberg UR - http://geodesic.mathdoc.fr/articles/10.1007/s10240-016-0087-3/ DO - 10.1007/s10240-016-0087-3 LA - en ID - PMIHES_2017__125__79_0 ER -
%0 Journal Article %A Cornulier, Yves %A Tessera, Romain %T Geometric presentations of Lie groups and their Dehn functions %J Publications Mathématiques de l'IHÉS %D 2017 %P 79-219 %V 125 %I Springer Berlin Heidelberg %C Berlin/Heidelberg %U http://geodesic.mathdoc.fr/articles/10.1007/s10240-016-0087-3/ %R 10.1007/s10240-016-0087-3 %G en %F PMIHES_2017__125__79_0
Cornulier, Yves; Tessera, Romain. Geometric presentations of Lie groups and their Dehn functions. Publications Mathématiques de l'IHÉS, Tome 125 (2017), pp. 79-219. doi: 10.1007/s10240-016-0087-3
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