A topological Tits alternative
By Emmanuel Breuillard, Tsachik Gelander. 2004
94 citations recorded by the source corpus.
Let k be a local eld, and GLn(k) a linear group over k. We prove that either contains a relatively open solvable subgroup, or it contains a relatively dense free subgroup. This result has applications in dynamics, Riemannian foliations and pronite groups.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/a107ddbde391e904909a598e14d91f59c1997919
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In Geometry and Topology
- Richard Aoun
- M. Kennedy
- Emmanuel Breuillard
- Tsachik Gelander
- Mehrdad Kalantar
- Nathanial P. Brown Narutaka Ozawa
- E. Guentner
- Sorin Popa
In Mathematical Physics
- M. Kennedy
- Emmanuel Breuillard
- Richard Aoun
- Tsachik Gelander
- Mehrdad Kalantar
- Nathanial P. Brown Narutaka Ozawa
- Gilles Pisier
- Adrian Ioana
Citations in the corpus
- Random subgroups of linear groups are free (2010, background): “A more conceptual proof can be found in [BG07] except that the representation ρ takes value in PGL(V ), and this is not enough for our purposes.”
- Uniform independence in linear groups (2006, methodology): “For a more exhaustive and detailed study of the dynamical properties of projective transformations, we refer the reader to [BG1], Section 3 and [ BG2 ], Section 3.”
- C*-simplicity and the unique trace property for discrete groups (2014, background): “d component of the identity of the closure Gof G in L. This conjecture was proved by Carri`ere and Ghys [14] for the case when Gis a free group, and by Zimmer [60] in general. Breuillard and Gelander [11,12] gave an alternative proof along the lines of Carri`ere and Ghys. We will give a new interpre”