14 papers
On transversality in flag manifolds and linearity of amalgams
Sami Douba, Konstantinos Tsouvalas
We show that the fundamental group of the double of a complete negatively curved locally symmetric manifold along a closed geodesic is linear. More generally, we establish linearit…
Directional growth of coamenable normal subgroups: counterexamples and rigidity
Subhadip Dey, Hee Oh, Konstantinos Tsouvalas
Roblin's theorem asserts that, in rank one, a coamenable normal subgroup has the same critical exponent as its ambient group. Natural higher-rank analogues would predict that coame…
Robust quasi-isometric embeddings of virtually free groups
Konstantinos Tsouvalas
Let be a nonarchimedean local field. For any , we construct the first examples of robust quasi-isometric embeddings of non-elementary free groups into $\mathsf{GL}_n(k…
Matrix entries, unipotents, and linearity of amalgams
Sami Douba, Konstantinos Tsouvalas
We investigate linearity of amalgams of subgroups of algebraic groups along intersections with algebraic subgroups. In the process, we establish linearity of certain "doubles" of l…
Undecidability of epimorphisms onto products of hyperbolic groups
Konstantinos Tsouvalas
We exhibit examples of finitely presented subgroups of direct products of hyperbolic groups for which there is no algorithm that detects whether a finitely presented group has…
Anosov representations, strongly convex cocompact groups and weak eigenvalue gaps
Konstantinos Tsouvalas
We provide characterizations of Anosov representations of word hyperbolic groups into real semisimple Lie groups in terms of the existence of equivariant limit maps on the Gromov b…