7 papers
Khovanov monodromy groups via motions
Gabriel Corrigan, Livio Ferretti, Isacco Nonino +1
For any link, we define a monodromy map from the motion group of the link to the group of automorphisms of the link's Khovanov homology. The image of this map is the \emph{unorient…
Extended signatures and link concordance
David Cimasoni, Livio Ferretti, Iuliia Popova
The Levine-Tristram signature admits an n-variable extension for n-component links: it was first defined as an integer valued function on , and recently exte…
A diagrammatic computation of abelian link invariants
David Cimasoni, Livio Ferretti, Jessica Liu
We show how the multivariable signature and Alexander polynomial of a colored link can be computed from a single symmetric matrix naturally defined from a colored link diagram. In…
On the Kashaev signature conjecture
David Cimasoni, Livio Ferretti
In 2018, Kashaev introduced a square matrix indexed by the regions of a link diagram, and conjectured that it provides a novel way of computing the Levine-Tristram signature and Al…
Two strand twisting
Lambert A'Campo, Sebastian Baader, Livio Ferretti +1
We prove that fibred knots cannot be untied with -moves, for all . More generally, we give an upper bound on the number of two strand twist operations that…
On the Jones polynomial modulo primes
Valeriano Aiello, Sebastian Baader, Livio Ferretti
We derive an upper bound on the density of Jones polynomials of knots modulo a prime number , within a sufficiently large degree range: . As an application, we classify k…
On Positive Braids, Monodromy Groups and Framings
Livio Ferretti
We associate to every positive braid a braid monodromy group, generalizing the geometric monodromy group of an isolated plane curve singularity. If the closure of the braid is a kn…