Universal lattices and property \(\tau\)

DOI10.1007/s00222-005-0498-0zbMath1139.19003arXivmath/0502112OpenAlexW2019345174MaRDI QIDQ2502045

Martin Kassabov, Nikolay Nikolov

Publication date: 12 September 2006

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0502112

Mathematics Subject Classification ID

Representation theory for linear algebraic groups (20G05) Unimodular groups, congruence subgroups (group-theoretic aspects) (20H05) Asymptotic properties of groups (20F69) Symbols, presentations and stability of (K_2) (19C20)

Related Items

Linear groups over general rings. I: Generalities., Property \((T)\) for noncommutative universal lattices, Relative property (T) and linear groups., On the congruence kernel of isotropic groups over rings, Property (𝑇) for Groups Graded by Root Systems, Characters of the group \(\mathrm{EL}_d (\mathcal{R})\) for a commutative Noetherian ring \(\mathcal{R}\), Finite simple groups of Lie type as expanders., Universal lattices and unbounded rank expanders., Golod-Shafarevich groups with property \((T)\) and Kac-Moody groups., Dimension expanders, The IA-congruence kernel of high rank free metabelian groups, The congruence subgroup problem for the free metabelian group on \(n\geq 4\) generators, On abstract homomorphisms of Chevalley groups over the coordinate rings of affine curves, Centrality of the congruence kernel for elementary subgroups of Chevalley groups of rank >1 over noetherian rings, Expander graphs in pure and applied mathematics, On semisimple representations of universal lattices., Non-expander Cayley Graphs of Simple Groups

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On a question of M. Newman on the number of commutators
• \(K_2\) of discrete valuation rings
• Presenting \(GL_n (k\langle T\rangle)\)
• On the groups \(\mathrm{SL}_ 2(\mathbb{Z}[x)\) and \(\mathrm{SL}_ 2(k[x,y])\)]
• Discrete groups, expanding graphs and invariant measures. Appendix by Jonathan D. Rogawski
• Random walk in random groups.
• Property (T) and Kazhdan constants for discrete groups
• Universal lattices and unbounded rank expanders.
• Solution of the congruence subgroup problem for \(\text{SL}_ n\) \((n\geq 3)\) and \(\text{Sp}_{2n}\) \((n\geq 2)\)
• Bounded Elementary Generation of SL n (O)
• KAZHDAN CONSTANTS FOR SL_n(ℤ)
• Higher algebraic K-theory: I
• Introduction to Algebraic K-Theory. (AM-72)
• ON THE STABILIZATION OF THE GENERAL LINEAR GROUP OVER A RING
• Surjective Stability in Dimension 0 for K 2 and Related Functors
• Bounded generation and Kazhdan's property (T)