Sh:818

• Kramer, L., Shelah, S., Tent, K., & Thomas, S. (2005). Asymptotic cones of finitely presented groups. Adv. Math., 193(1), 142–173. arXiv: math/0306420 DOI: 10.1016/j.aim.2004.04.012 MR: 2132762
• Abstract:
  Let $G$ be a connected semisimple Lie group with at least one absolutely simple factor $S$ such that ${\mathbb R}\text{-rank}(S) \geq 2$ 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.

• published version (32p)

@article{Sh:818,
 author = {Kramer, Linus and Shelah, Saharon and Tent, Katrin and Thomas, Simon},
 title = {{Asymptotic cones of finitely presented groups}},
 journal = {Adv. Math.},
 fjournal = {Advances in Mathematics},
 volume = {193},
 number = {1},
 year = {2005},
 pages = {142--173},
 issn = {0001-8708},
 mrnumber = {2132762},
 mrclass = {20F65 (54D80)},
 doi = {10.1016/j.aim.2004.04.012},
 note = {\href{https://arxiv.org/abs/math/0306420}{arXiv: math/0306420}},
 arxiv_number = {math/0306420}
}