Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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Transverse invariants from sl_3 homologies

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 S3 (endowed with the symmetric contact structure) arising from the deformations of Khovanov sl3 homology.

I will start with a brief introduction to the theory of transverse links in S3. 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 sl3 link homology, due to Mackaay and Vaz, and define the transverse invariants. These invariants, which are called the \beta3-invariants, are cycles in the universal sl3 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 \beta3-invariants.

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