arXiv subjects

R. Spitler

Publications and source records attributed to R. Spitler.

3 recordsLinked to original sources

arXiv2023

Absolute profinite rigidity, direct products, and finite presentability

We prove that there exist finitely presented, residually finite groups that are profinitely rigid in the class of all finitely presented groups but not in the class of all finitely generated groups. These groups are of the form $\Gamma \times \Gamma$ where $\Gamma$ is a profinitely rigid 3-manifold group; we describe a family of such groups with the property that if $P$ is a finitely generated, residually finite group with $\widehat{P}\cong\widehat{\Gamma\times\Gamma}$ then there is an embedding $P\hookrightarrow\Gamma\times\Gamma$ that induces the profinite isomorphism; in each case there are infinitely many non-isomorphic possibilities for $P$.

math.GR↗

arXiv2020

On the profinite rigidity of triangle groups

We prove that certain Fuchsian triangle groups are profinitely rigid in the absolute sense, i.e. each is distinguished from all other finitely generated, residually finite groups by its set of finite quotients. We also develop a method based on character varieties that can be used to distinguish between the profinite completions of certain groups.

math.GR↗

arXiv2018

Absolute profinite rigidity and hyperbolic geometry

We construct arithmetic Kleinian groups that are profinitely rigid in the absolute sense: each is distinguished from all other finitely generated, residually finite groups by its set of finite quotients. The Bianchi group $\mathrm{PSL}(2,\mathbb{Z}[\omega])$ with $\omega^2+\omega+1=0$ is rigid in this sense. Other examples include the non-uniform lattice of minimal co-volume in $\mathrm{PSL}(2,\mathbb{C})$ and the fundamental group of the Weeks manifold (the closed hyperbolic $3$-manifold of minimal volume).

math.GT↗