Dehn function and asymptotic cones of Abels' group
Group Theory
2014-03-07 v2
Abstract
We prove that Abels' group over an arbitrary nondiscrete locally compact field has a quadratic Dehn function. As applications, we exhibit connected Lie groups and polycyclic groups whose asymptotic cones have uncountable abelian fundamental group. We also obtain, from the case of finite characteristic, uncountably many non-quasi-isometric finitely generated solvable groups, as well as peculiar examples of fundamental groups of asymptotic cones.
Cite
@article{arxiv.1203.4696,
title = {Dehn function and asymptotic cones of Abels' group},
author = {Yves Cornulier and Romain Tessera},
journal= {arXiv preprint arXiv:1203.4696},
year = {2014}
}
Comments
34 pages, no figure (v2: various corrections and minor improvements especially in the last section)