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

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.

knot, Khovanov homology, cable link, Rasmussen invariant
Mathematical Subject Classification 2010
Primary: 57M27
Secondary: 57M25
Received: 23 October 2012
Revised: 16 March 2013
Accepted: 17 April 2013
Published: 20 July 2013
Keiji Tagami
Department of Mathematics
Tokyo Institute of Technology
Ookayama, Meguro
Tokyo 152-8551