On the Transverse Khovanov-Rozansky Homologies: Graded Module Structure and Stabilization

Abstract

In arXiv:1308.3152, the author proved that the Khovanov-Rozansky homology ${\mathcal{H}}_N$ with potential $a{x}^{N+1}$ is an invariant for transverse links in the standard contact $3$-sphere. In the current paper, we study the ${\mathbb{Z}}_2\oplus {\mathbb{Z}}^{\oplus 3}$-graded $\mathbb{Q}[a]$-module structure of ${\mathcal{H}}_N$, which leads to better understanding of the effect of stabilization on ${\mathcal{H}}_N$. As an application, we compute ${\mathcal{H}}_N$ for all transverse unknots.

21 pages, 7 figures. arXiv admin note: text overlap with arXiv:1308.3152

References in corpus (1)

• The Markov Theorem for transverse knots