Seminário de Teoria Quântica do Campo Topológica  

05/06/2006, 15:30 — 16:30 — Sala P3.10, Pavilhão de Matemática
Marko Stosic, Instituto Superior Técnico

Khovanov homology of torus knots

In this talk we show that the torus knots $T_{p,q}$ for $3\le p\le q$ are homologically thick. Furthermore, we show that we can reduce the number of twists $q$ without changing a certain part of the homology, and consequently we show that there exists a stable homology for torus knots conjectured in [1]. Also, we calculate the Khovanov homology groups of low homological degree for torus knots, and we conjecture that the homological width of the torus knot $T_{p,q}$ is at least $p$.

References:

[1] N. Dunfield, S. Gukov and J. Rasmussen: The Superpolynomial for link homologies, arXiv:math.GT/0505056.

[2] M. Stosic: Homological thickness of torus knots, arXiv:math.GT/0511532