2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/105024In 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 pagesQuantum Algebra57M25text