TY - JOUR
T1 - Asymptotic cones of finitely presented groups
AU - Kramer, Linus
AU - Shelah, Saharon
AU - Tent, Katrin
AU - Thomas, Simon
N1 - Funding Information:
$The research of L.K. and K.T. was supported by Heisenberg Fellowships of the DFG. The research of S.S. was supported by the Israel Science Foundation. This paper is number 818 in the cumulative list of the S.S.’s publications. The research of S.T. was partially supported by NSF Grants. ·Corresponding author. E-mail addresses: [email protected] (L. Kramer), [email protected] (S. Shelah), [email protected] (K. Tent), [email protected] (S. Thomas).
PY - 2005/5/1
Y1 - 2005/5/1
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
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U2 - 10.1016/j.aim.2004.04.012
DO - 10.1016/j.aim.2004.04.012
M3 - Article
AN - SCOPUS:13844255300
SN - 0001-8708
VL - 193
SP - 142
EP - 173
JO - Advances in Mathematics
JF - Advances in Mathematics
IS - 1
ER -