Dehn function and asymptotic cones of Abels' group

Details Dehn function and asymptotic cones of Abels' group Dehn function and asymptotic cones of Abels' group

2012-03-21

arxiv.org/abs/1203.4696v1

Mathematics

Group Theory

28 pages, no figure

Scientific paper

We prove that Abels' group over an arbitrary local 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.

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