Authors: Stošić, Marko 
Title: Khovanov homology of torus links
Journal: Topology and its Applications
Volume: 156
Issue: 3
First page: 533
Last page: 541
Issue Date: 1-Jan-2009
Rank: M23
ISSN: 0166-8641
DOI: 10.1016/j.topol.2008.08.004
Abstract: 
In this paper we show that there is a cut-off in the Khovanov homology of (2 k, 2 k n)-torus links, namely that the maximal homological degree of non-zero homology groups of (2 k, 2 k n)-torus links is 2 k2 n. Furthermore, we calculate explicitly the homology group in homological degree 2 k2 n and prove that it coincides with the center of the ring Hk of crossingless matchings, introduced by M. Khovanov in [M. Khovanov, A functor-valued invariant for tangles, Algebr. Geom. Topol. 2 (2002) 665-741, arXiv:math.QA/0103190]. This gives the proof of part of a conjecture by M. Khovanov and L. Rozansky in [M. Khovanov, L. Rozansky, A homology theory for links in S2 × S1, in preparation]. Also we give an explicit formula for the ranks of the homology groups of (3, n)-torus knots for every n ∈ N.
Keywords: Hochschild cohomology | Khovanov homology | Torus knots
Publisher: Elsevier
Project: FEDER, project Quantum Topology POCI/MAT/60352/2004
Ministry of Science of Serbia, project 144032

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