Asymptotic cones of finitely presented groups

Linus Kramer; Saharon Shelah; Katrin Tent; Simon Thomas

Asymptotic cones of finitely presented groups

Geometric Topology 2007-05-23 v2 Group Theory

Authors: Linus Kramer , Saharon Shelah , Katrin Tent , Simon Thomas

Abstract

Let G be a connected semisimple Lie group with at least one absolutely simple factor S such that R-rank(S) is at least 2, and let $\Gamma$ be a uniform lattice in G. (a) If $CH$ holds, then $\Gamma$ has a unique asymptotic cone up to homeomorphism. (b) If $CH$ fails, then $\Gamma$ has $2^{2^{\omega}}$ asymptotic cones up to homeomorphism.

Keywords

group theory convex cones asymptotic analysis

Cite

@article{arxiv.math/0306420,
  title  = {Asymptotic cones of finitely presented groups},
  author = {Linus Kramer and Saharon Shelah and Katrin Tent and Simon Thomas},
  journal= {arXiv preprint arXiv:math/0306420},
  year   = {2007}
}

Comments

To appear in Advances in Mathematics

Asymptotic cones of finitely presented groups

Abstract

Keywords

Cite

Comments

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