Related papers: Determining knot groups by finite quotients

We show that hyperbolic four-punctured $S^2-$bundles over $S^1$ are distinguished by the finite quotients of their fundamental groups among all 3-manifold groups. To do this, we upgrade a result of Liu to show that the topological type of a…

There has been much recent interest into those properties of a 3-manifold determined by the profinite completion of its fundamental group. In this paper we give readily computable criteria specifying precisely when two orientable graph…

We show that a regular isomorphism of profinite completion of the fundamental groups of two 3-manifolds $N_1$ and $N_2$ induces an isometry of the Thurston norms and a bijection between the fibered classes. We study to what extent does the…

Any profinite isomorphism between two cusped finite-volume hyperbolic 3-manifolds carries profinite isomorphisms between their Dehn fillings. With this observation, we prove that some cusped finite-volume hyperbolic 3-manifolds are…

We exhibit an algorithm to determine the bridge number of a hyperbolic knot in the 3-sphere. The proof uses adaptations of almost normal surface theory for compact surfaces with boundary in ideally triangulated knot exteriors.

This note surveys recent progress toward the profinite rigidity of orientable finite-volume hyperbolic 3-manifolds. Beginning in a brief review of some basic settings of profinite completion and rigidity of general groups, we state the…

We establish results concerning the profinite completions of 3-manifold groups. In particular, we prove that the complement of the figure-eight knot $S^3-K$ is distinguished from all other compact 3-manifolds by the set of finite quotients…

We analyze the orbifolds that can be obtained as quotients of hyperbolic 3-manifolds admitting a Heegaard splitting of genus two by their orientation preserving isometry groups. The genus two hyperbolic 3-manifolds are exactly the…

In this paper we study some consequences of the author's classification of graph manifolds by their profinite fundamental groups. In particular we study commensurability, the behaviour of knots, and relation to mapping classes. We prove…

We give the first examples of closed fibered hyperbolic 3-manifolds whose fundamental groups are distinguished from every other finitely generated, residually finite group by their finite quotients. One of the examples is also the first…

We prove that any isomorphism between the profinite completions of the fundamental groups of two cusped finite-volume hyperbolic 3-manifolds is regular and peripheral regular. As an application, we show that the $A$-polynomial of prime…

It is known that any tame hyperbolic 3-manifold with infinite volume and a single end is the geometric limit of a sequence of finite volume hyperbolic knot complements. Purcell and Souto showed that if the original manifold embeds in the…

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 $p$, then $H$ is virtually soluble, and…

The isometry group of a compact n-dimensional hyperbolic manifold is known to be finite. We show that for every n > 2, every finite group is realized as the full isometry group of some compact hyperbolic n-manifold. The cases n = 2 and n =…

We give a criterion for distinguishing a prime knot $K$ in $S^3$ from every other knot in $S^3$ using the finite quotients of $\pi_1(S^3\setminus K)$. Using recent work of Baldwin-Sivek, we apply this criterion to the hyperbolic knots…

For any orientable finite-volume hyperbolic 3-manifold, this paper proves that the profinite isomorphism type of the fundamental group uniquely determines the isomorphism type of the first integral cohomology, as marked with the Thurston…

We show that a hyperbolic 2-bridge knot complement is the unique knot complement in its commensurability class. We also discuss constructions of commensurable hyperbolic knot complements and put forth a conjecture on the number of…

We identify all hyperbolic knots whose complements are in the census of orientable one-cusped hyperbolic manifolds with eight ideal tetrahedra. We also compute their Jones polynomials.

We prove that if two cusped hyperbolic $3$-manifolds admit a regular isomorphism between the profinite completions of their fundamental groups, then they share the same $A$-polynomial and their strongly detected boundary slopes match up.

We prove that there are compact submanifolds of the 3-sphere whose interiors are not homeomorphic to any geometric limit of hyperbolic knot complements.