Asymptotic cones of finitely presented groups

Linus Kramer; Saharon Shelah; Katrin Tent; Simon Thomas

doi:10.1016/j.aim.2004.04.012

Asymptotic cones of finitely presented groups

Linus Kramer
, Saharon Shelah
, Katrin Tent
, Simon Thomas^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

Abstract

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 2^2ω asymptoticones up to homeomorphism.

Original language	English
Pages (from-to)	142-173
Number of pages	32
Journal	Advances in Mathematics
Volume	193
Issue number	1
DOIs	https://doi.org/10.1016/j.aim.2004.04.012
State	Published - 1 May 2005

Keywords

Affine buildings
Asymptotic cone
Finitely presented groups

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10.1016/j.aim.2004.04.012

Cite this

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title = "Asymptotic cones of finitely presented groups",

abstract = "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 asymptoticones up to homeomorphism.",

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AU - Kramer, Linus

AU - Shelah, Saharon

AU - Tent, Katrin

AU - Thomas, Simon

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N2 - 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 asymptoticones up to homeomorphism.

AB - 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 asymptoticones up to homeomorphism.

KW - Affine buildings

KW - Asymptotic cone

KW - Finitely presented groups

UR - https://www.scopus.com/pages/publications/13844255300

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VL - 193

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JO - Advances in Mathematics

JF - Advances in Mathematics

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Asymptotic cones of finitely presented groups

Abstract

Keywords

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