Properties of Khovanov homology for positive braid knots

Abstract

In this paper we solve one open problem from \cite{pat} and give some generalizations. Namely, we prove that the first homology group of positive braid knot is trivial. Also, we show that the same is true for the Khovanov-Rozansky homology \cite{kovroz} ($sl(n)$ link homology) for any positive integer $n$.

12 pages