Asymptotic cones of finitely presented groups

By L. Kramer, Saharon Shelah, K. Tent, S. Thomas. 2003

51 citations recorded by the source corpus.

Let G be a connected semisimple Lie group with at least one absolutely simple factor S such that R-rank(S)⩾2 and let Γ be a uniform lattice in G. (a) If CH holds, then Γ has a unique asymptotic cone up to homeomorphism. (b) If CH fails, then Γ has 22ω asymptotic cones up to homeomorphism.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4f2458b261ae03ab8d13baa3c3c9203d5ca53eee

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Lacunary hyperbolic groups (2007, background): “Note that finitely presented groups with different asymptotic cones were constructed in [44] (earlier, in [32], such groups were found under the assumption that the Continuum Hypothesis does not hold).”
Dimension of asymptotic cones of Lie groups (2007, background): “However, it is not known if a connected Lie group can have two non-homeomorphic asymptotic cones; nevertheless in [ KSTT , KrTe] it is proved that an absolutely simple group of real rank at least two has a unique asymptotic cone up to homeomorphism if and only if the continuum hypothesis is true.”
Asymptotic Geometry of the Mapping Class Group and Teichmuller Space (2005, background): “K; C /–quasi-isometric and denote this X K ;C Y ; When the choice of constants is not important (as will often be the case), we simply say X and Y are quasi-isometric, denoted X Y .”