Related papers: Virtual pro-$p$ properties of 3-manifold groups

We examine three key conjectures in 3-manifold theory: the virtually Haken conjecture, the positive virtual b_1 conjecture and the virtually fibred conjecture. We explore the interaction of these conjectures with the following seemingly…

Let $M$ be a closed, orientable, irreducible, geometrizable 3-manifold. We prove that the profinite topology on the fundamental group of $\pi_1(M)$ is efficient with respect to the JSJ decomposition of $M$. We go on to prove that $\pi_1(M)$…

We construct examples of groups showing that virtual solvability and the property of being virtually torsion-free are not preserved by bi-Lipschitz maps and hence by quasi-isometries.

This article has two purposes. In \cite{R3} (math.KT/0405211) we showed that the FIC (Fibered Isomorphism Conjecture for pseudoisotopy functor) for a particular class of 3-manifolds (we denoted this class by \cal C) is the key to prove the…

In this paper, we mainly discuss the representations of closed graph manifolds to the Seifert motion group. Then we prove that there exist graph manifolds virtually having no faithful representations to the Seifert motion group.

In this work, we consider relative character varieties for representations of the 3-punctured sphere group in PU(2,1). We provide necessary and sufficient conditions on the peripheral conjugacy classes, for such a representation to admit a…

Let $p:F\to G$ be a morphism of stacks of positive \emph{virtual} relative dimension $k$ and let $\gamma\in H^k(F)$. We give sufficient conditions for $p_*\gamma\cdot[F]^{virt}$ to be a multiple of $[G]^{virt}$. We apply this result to show…

We study combinatorial properties of virtual braid groups and we describe relations with finite type invariant theory for virtual knots and Yang-Baxter equations

We completely describe the finitely generated pro-$p$ subgroups of the profinite completion of the fundamental group of an arbitrary $3$-manifold. We also prove a pro-$p$ analogue of the main theorem of Bass--Serre theory for finitely…

We prove that the Bredon cohomological dimension and the virtual cohomological dimension coincide for groups that admit a cocompact model for $\underline{E}G$ and satisfy properties (M) and (NM). Among the examples of groups satisfying…

We extend two results known for aspherical 3-manifolds to $PD_3$-pairs $(P,\partial{P})$ with aspherical ambient space $P$. Every such $PD_3$-pair may be assembled by attaching 1-handles to $PD_3$-pairs with aspherical; ambient space and…

Recently, Schlage-Puchta proved super multiplicity of $p$-deficiency for normal subgroups of $p$-power index. We extend this result to all normal subgroups of finite index. We then use the methods of the proof to show that some groups with…

In this paper, it is shown that for any closed orientable $3$-manifold with positive simplicial volume, the growth of the Seifert volume of its finite covers is faster than the linear rate. In particular, each closed orientable $3$-manifold…

In recent years, the RFRS condition has been used to analyze virtual fibering in 3-manifold topology. Agol's work shows that any 3-manifold with zero Euler characteristic satisfying the RFRS condition on its fundamental group virtually…

It is shown in this paper that given any closed oriented hyperbolic 3-manifold, every closed oriented 3-manifold is mapped onto by a finite cover of that manifold via a map of degree 1, or in other words, virtually 1-dominated by that…

We prove that if a prime 3-manifold M is not finitely covered by the 3-sphere or a product manifold, then M is virtually chiral, i.e. it has a finite cover that does not admit an orientation reversing self-homeomorphism. In general if a…

L. Kauffman (2024) introduced multi-virtual and symmetric multi-virtual braid groups, which are generalizations of the virtual braid group. We introduce multi-virtual pure and multi-virtual semi-pure braid groups, which are normal subgroups…

In this paper we deal with Seifert fibre spaces, which are compact 3-manifolds admitting a foliation by circles. We give a combinatorial description for these manifolds in all the possible cases: orientable, non-orientable, closed, with…

The Evasiveness conjecture have been proved for properties of graphs on a prime-power number of vertices and the six vertices case. The ten vertices case is still unsolved. In this paper we study the size of the automorphism group 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…