Quantification of separability of cubically convex-cocompact subgroups of RAAGs via representations (Olga Kharlampovich, CUNY, Graduate Center and Hunter College)

07.05.2024 10:30

We answer the question asked by Louder, McReinolds and Patel and prove the following statement. Let L be a RAAG, H a cubically convex-cocompact subgroup of L, then there is a finite dimensional representation of L that separates the subgroup H in the induced Zariski topology. As a corollary, we establish a polynomial upper bound on the size of the quotients used to separate H in L. This implies the same statement for a virtually special group L and, in particular, a fundamental group of a hyperbolic 3-manifold.
For any finitely generated subgroup H of a limit group L we prove the same results and, in addition, show that there exists a finite-index subgroup K containing H, such that K is a subgroup of a group obtained from H by a series of extensions of centralizers and free products with infinite cyclic group. If H is non-abelian, the K is fully residually H. A corollary is that a hyperbolic limit group satisfies the Geometric Hanna Neumann conjecture. These are joint results with K. Brown and A. Vdovina.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-05, Tuesday 07.05.2024, Séminaire "Groupes et géométrie"

entrée libre