• Corpus ID: 253761506

On the profinite rigidity of free and surface groups

  title={On the profinite rigidity of free and surface groups},
  author={Ismael Morales},
. Let S be a free or surface group. We establish a Tits alternative for groups in the finite, soluble and p -genus of S . This generalises (and gives a new proof of) the analogous result of Baumslag for parafree groups. Then we study applications to profinite rigidity. A well-known question of Remeslennikov asks whether a finitely generated residually finite G with profinite completion b G ∼ = b S is necessarily G ∼ = S . We give a positive answer when G belongs to a class of groups H ab that has a… 



Characterising surface groups by their virtual second betti number

. Define the virtual second betti number of a finitely generated group G as vb 2 ( G ) = sup { dim H 2 ( H ; Q ) | H ≤ G of finite index } ∈ Z ≥ 0 ∪ {∞} . We show that if G is a one-ended

A “Tits-alternative” for subgroups of surface mapping class groups

. It has been observed that surface mapping class groups share various properties in common with the class of linear groups (e.g., [BLM, H]). In this paper, the known list of such properties is

Essential surfaces in graph pairs

  • H. Wilton
  • Mathematics
    Journal of the American Mathematical Society
  • 2018
A well-known question of Gromov asks whether every one-ended hyperbolic group Γ \Gamma has a surface subgroup. We give a positive answer when Γ \Gamma is the fundamental group of

Distinguishing geometries using finite quotients

We prove that the profinite completion of the fundamental group of a compact 3-manifold $M$ satisfies a Tits alternative: if a closed subgroup $H$ does not contain a free pro-$p$ subgroup for any

Free Subgroups of Linear Groups

Note that from the definition immediately follows that the group G is a free group with free generators gi, i ∈ I. Indeed, let g = g1 i1 . . . g mk ik be any reduced word. Take p ∈ D0, then gp ∈ D±

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Previously, the authors proved that the presentation complex of a onerelator group G satisfies a geometric condition called negative immersions if every two-generator, one-relator subgroup of G is

Tits alternatives for graph products

We discuss various types of Tits Alternative for subgroups of graph products of groups, and prove that, under some natural conditions, a graph product of groups satisfies a given form of Tits

The profinite completion of relatively hyperbolic virtually special groups

We give a characterization of toral relatively hyperbolic virtually special groups in terms of the profinite completion. We also prove a Tits alternative for subgroups of the profinite completion b G


We establish some sufficient conditions for the profinite and pro-p completions of an abstract group G of type FP m (resp. of finite cohomological dimension, of finite Euler characteristic) to be of