We give a short introduction to the theory of twisted Alexander polynomials of a 3-manifold
associated to a representation of its fundamental group. We summarize their formal …

We study a twisted Alexander polynomial naturally associated to a hyperbolic knot in an
integer homology 3-sphere via a lift of the holonomy representation to. It is an unambiguous …

A classical result in knot theory says that for a fibered knot the Alexander polynomial is
monic and that the degree equals twice the genus of the knot. This result has been …

We show that given any 3-manifold N and any non-fibered class in H1 (N; Z) there exists a
representation such that the corresponding twisted Alexander polynomial is zero. We obtain …

This paper gives an explicit formula for the SL2 (ℂ)-non-abelian Reidemeister torsion as
defined in [6] in the case of twist knots. For hyperbolic twist knots, we also prove that the non …

Profinite rigidity of fibring Page 1 Rev. Mat. Iberoam. (Online first) DOI 10.4171/RMI/1524 ©
2025 Real Sociedad Matemática Española Published by EMS Press Profinite rigidity of fibring …

The Alexander polynomial of a knot has been generalized in three different ways to give
twisted invariants. The resulting invariants are usually referred to as twisted Alexander …

We prove that twisted ℓ 2-Betti numbers of locally indicable groups are equal to the usual ℓ 2-
Betti numbers rescaled by the dimension of the twisting representation; this answers a …

We prove that amongst the class of free-by-cyclic groups, Gromov hyperbolicity is an
invariant of the profinite completion. We show that whenever $ G $ is a free-by-cyclic group …

Given a knot and an SL n F representation of its group that is conjugate to its dual, the
representation that replaces each matrix with its inverse-transpose, the associated twisted …