Geodesic
The maximal degree of the Khovanov homology of a cable link
Tagami, Keiji1
1Department of Mathematics, Tokyo Institute of Technology, Ookayama, Meguro, Tokyo 152-8551, Japan
Algebraic and Geometric Topology, Tome 13 (2013) no. 5, pp. 2845-2896
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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 (2k+1,(2k+1)n)–torus link and give a lower bound of its homological thickness. Specifically, we show that the homological thickness of the (2k + 1,(2k + 1)n)–torus link is greater than or equal to k2n + 2. Next, we study the maximal homological degree of the Khovanov homology of the (p,pn)–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.

DOI : 10.2140/agt.2013.13.2845
Classification : 57M27, 57M25
Keywords: knot, Khovanov homology, cable link, Rasmussen invariant

Tagami, Keiji  1

1 Department of Mathematics, Tokyo Institute of Technology, Ookayama, Meguro, Tokyo 152-8551, Japan 
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Tagami, Keiji. The maximal degree of the Khovanov homology of a cable link. Algebraic and Geometric Topology, Tome 13 (2013) no. 5, pp. 2845-2896. doi: 10.2140/agt.2013.13.2845

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