Expansion in SLd(Z/qZ), q arbitrary

By Jean Bourgain, P. P. Varj'u. 2010

80 citations recorded by the source corpus.

Let S be a fixed finite symmetric subset of SLd(Z), and assume that it generates a Zariski-dense subgroup G. We show that the Cayley graphs of πq(G) with respect to the generating set πq(S) form a family of expanders, where πq is the projection map Z→Z/qZ.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/c47722c90c0b4ca92cceee58374a384bb17a7b86

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In Discrete Mathematics and Combinatorics

1. Adrian Ioana

In Geometry and Topology

1. Adrian Ioana
2. S. Vaes
3. Sorin Popa
4. J. Peterson
5. Damien Gaboriau
6. Thomas Sinclair
7. A. Furman

Citations in the corpus

• RIGIDITY FOR VON NEUMANN ALGEBRAS (2017, methodology): “This was recently generalized in Bourgain and Varjú [2012] to arbitrary nonamenable subgroups Γ < SL2(Z): the left translation of Γ onto its closure Γ̄ < SL2(Zp) has spectral gap. Note that in Furman [2011], Furman provided an alternative approach to part (1) of Theorem 5.”