## 16/07/2010, Friday, 10:00–11:00

Yasuyoshi Yonezawa, Univ. of the Algarve and IST
Quantum $\left({\mathrm{sl}}_{n},\wedge {V}_{n}\right)$ link invariant and matrix factorizations.

M. Khovanov and L. Rozansky constructed a homology for a link diagram whose Euler characteristic is the quantum link invariant associated to the quantum group $\mathrm{Uq}\left({\mathrm{sl}}_{n}\right)$ and its vector representation ${V}_{n}$ by using matrix factorizations. In my thesis, I study a generalization of the Khovanov-Rozansky homology for the quantum link invariant associated to $\mathrm{Uq}\left({\mathrm{sl}}_{n}\right)$ and its fundamental representations $\wedge {V}_{n}$. In this talk, I will define a new link invariant derived from the generalization of Khovanov-Rozansky homology.
Support: FCT, CAMGSD, New Geometry and Topology