The word and Riemannian metrics on lattices of semisimple groups

By A. Lubotsky, Shahar Mozes, M. Raghunathan, Henryk Iwaniec, Wenzhi Luo, Peter Sarnak, L. Stolovitch. 2000

166 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b241c31281f2bcd9b5cc3f0a0428f8ea5207897c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Indira Chatterji
2. Yehuda Shalom
3. Kai-Uwe Bux
4. Kim Ruane
5. George A. Willis
6. Nikolai V. Ivanov
7. Sorin Popa
8. Y. Kida

In Mathematical Physics

1. Indira Chatterji
2. Yehuda Shalom
3. George A. Willis
4. Kai-Uwe Bux
5. Kim Ruane
6. Nikolai V. Ivanov
7. Nicolas Monod
8. Y. Kida

Citations in the corpus

• Fifteen problems about the mapping class groups (2006, methodology): “). Inthe arithmetic groupscase, thelogarithmic growth corresponds tovirtually unipotent elements of arithmetic groups of rank ≥ 2, according to a theorem of A. Lubotzky, S. Moses and M.S. Raghunathan [LMR]. B. Farb, A. Lubotzky and Y. Minsky [FLM] proved that the growth is linear, so the problem is ”
• Finiteness properties of arithmetic groups over function fields (2004, background): “FP∞ if it acts cocompactly on XΓ .I fΓ does not act cocompactly, then Theorems 1.1 and 1.4 (along with Corollary 7.3 of [ Lu ]) characterize those Γ contained in semisimple groups over function fields as precisely those which fail to be of typeFP∞.”
• Quantifying residual finiteness (2008, background): “t contain any principal congruence subgroups is said to be essential. Theorem 2.7. If k>2, then FSL k(O L)(n) n. Proof. We first pick a candidate for the lower bound. By Lubotzky-MozesRaghunathan [4], Theorem A, there exists a finite generating set, S, for SLk(Z) (see also Riley [6]) and a C>0 ”
• Commensurated Subgroups of Arithmetic Groups, Totally Disconnected Groups and Adelic Rigidity (2009, methodology): “Of course, with some more structural theoretic arguments (along the same lines of [24]) this result can also be proved using the approach taken in the proof of Theorem 1.”
• Some geometric groups with Rapid Decay (2003, background): “∈Bℓ(e,r) |f(γ)|2 ≤ P(r)kfk2, the second inequality being just the Cauchy-Schwartz inequality, and the last inequality is polynomial growth. According to A. Lubotzky, S. Mozes and M. S. Raghunathan in [35] there exists an infinite cyclic subgroup growing exponentially with respect to the word length i”