2 citations · 4 across the 8 of their papers we have counts for
8 papers
Multisections of higher-dimensional manifolds
Fathi Ben Aribi, Sylvain Courte, Marco Golla +1
Generalizing Heegaard splittings of 3-manifolds and trisections of 4-manifolds, we consider multisections of higher-dimensional smooth (or PL) closed orientable manifolds, namely d…
Fuglede-Kadison determinants over free groups and Lehmer's constants
Fathi Ben Aribi
Lehmer's famous problem asks whether the set of Mahler measures of polynomials with integer coefficients admits a gap at 1. In 2019, Lück extended this question to Fuglede-Kadison…
The Chen-Yang volume conjecture for knots in handlebodies
Fathi Ben Aribi, James Gosselet
In 2015, Chen and Yang proposed a volume conjecture that stated that certain Turaev-Viro invariants of an hyperbolic 3-manifold should grow exponentially with a rate equal to the h…
Link invariants from -Burau maps of braids
Fathi Ben Aribi
A previous work of A. Conway and the author introduced -Burau maps of braids, which are generalizations of the Burau representation whose coefficients live in a more general g…
Geometric triangulations and the Teichmüller TQFT volume conjecture for twist knots
Fathi Ben Aribi, François Guéritaud, Eiichi Piguet-Nakazawa
We construct a new infinite family of ideal triangulations and H-triangulations for the complements of twist knots, using a method originating from Thurston. These triangulations p…
The leading coefficient of the -Alexander torsion
Fathi Ben Aribi, Stefan Friedl, Gerrit Herrmann
We give upper and lower bounds on the leading coefficients of the -Alexander torsions of a -manifold in terms of hyperbolic volumes and of relative -torsions of su…
-Burau maps and -Alexander torsions
Fathi Ben Aribi, Anthony Conway
It is well known that the Burau representation of the braid group can be used to recover the Alexander polynomial of the closure of a braid. We define -Burau maps and use them…
Gluing formulas for the -Alexander torsions
Fathi Ben Aribi
We prove a Torres-like formula for the -Alexander torsions of links, as well as formulas for connected sums and cablings of links. Along the way we compute explicitly the $L^2…