#### Volume 13, issue 5 (2013)

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The maximal degree of the Khovanov homology of a cable link

### Keiji Tagami

Algebraic & Geometric Topology 13 (2013) 2845–2896
##### Abstract

In this paper, we study the Khovanov homology of cable links. We first estimate the maximal homological degree term of the Khovanov homology of the $\left(2k+1,\left(2k+1\right)n\right)$–torus link and give a lower bound of its homological thickness. Specifically, we show that the homological thickness of the $\left(2k+1,\left(2k+1\right)n\right)$–torus link is greater than or equal to ${k}^{2}n+2$. Next, we study the maximal homological degree of the Khovanov homology of the $\left(p,pn\right)$–cabling of any knot with sufficiently large $n$. Furthermore, we compute the maximal homological degree term of the Khovanov homology of such a link with even $p$. As an application we compute the Khovanov homology and the Rasmussen invariant of a twisted Whitehead double of any knot with sufficiently many twists.

##### Keywords
knot, Khovanov homology, cable link, Rasmussen invariant
Primary: 57M27
Secondary: 57M25