Dehn function and asymptotic cones of Abels' group

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.

34 pages, no figure (v2: various corrections and minor improvements especially in the last section)

References in corpus (1)

• Metabelian groups with quadratic Dehn function and Baumslag-Solitar groups

Cited by in corpus (9)

• Speed of random walks, isoperimetry and compression of finitely generated groups
• Geometric presentations of Lie groups and their Dehn functions
• Quasi-isometric diversity of marked groups
• About the speed of random walks on solvable groups
• On the finiteness length of some soluble linear groups
• Asymptotic cones of HNN extensions and amalgamated products
• Amenable groups without finitely presented amenable covers
• The Dehn function of Sp(2n;Z)
• Densely related groups