Buondì,
Vi segnalo il seminario di geometria di giovedì prossimo (ore 16 aula
seminari). Siete tutti invitati,
A presto,
Bruno Martelli
Thursday, October 4, 2018 16:00 17:00
SEMINARI DI GEOMETRIA
Sala Seminari (Dip. Matematica)
Transverse invariants from the deformations of Khovanov sl_3 homology
Carlo Collari
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.