Carlo Collari
(Department of Mathematical Sciences, Durham University)

created by daniele on 04 Dec 2018 modified on 10 Dec 2018

11 dec 2018
-- 12:00

Aula Tricerri, DiMaI, Firenze

Abstract.

In this talk I will describe some invariants for transverse links in
S^{3} (endowed with the symmetric contact structure) arising from the
deformations of Khovanov sl_{3} homology.

I will start with a brief introduction to the theory of transverse
links in S^{3.} Afterward, I will recall some known results concerning
transverse invariants in link homologies. In particular, I will focus
on the invariants coming from Khovanov-Rozansky homologies, and those
coming from the deformations of Khovanov homology.

After the introductory part, I will briefly describe the construction
and the properties of the universal sl_{3} link homology, due to Mackaay
and Vaz, and define the transverse invariants. These invariants, which
are called the \beta_{3}-invariants, are cycles in the universal sl_{3}
complex.

Finally, I will state a result concerning the vanishing of the
homology classes of these invariants, and compare it with similar
results known for other invariants. The idea of the proof will be also
given. Time permitting, I will also give a number of Bennequin-type
inequalities which can be proved using the \beta_{3}-invariants.