Khovanov homology of torus links

被引:21
作者
Stosic, Marko [1 ,2 ]
机构
[1] Inst Sistemas & Robot, P-1049001 Lisbon, Portugal
[2] Univ Tecn Lisboa, CAMGSD, Inst Super Tecn, P-1049001 Lisbon, Portugal
关键词
Khovanov homology; Torus knots; Hochschild cohomology; COHOMOLOGY; THICKNESS;
D O I
10.1016/j.topol.2008.08.004
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper we show that there is a cut-off in the Khovanov homology of (2k, 2kn)-torus links, namely that the maximal homological degree of non-zero homology groups of (2k, 2kn)-torus links is 2k(2)n. Furthermore, we calculate explicitly the homology group in homological degree 2k2n and prove that it coincides with the center of the ring H-k 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 S-2 x S-1, in preparation]. Also we give an explicit formula for the ranks of the homology groups of (3, n)-torus knots for every n epsilon N. (C) 2008 Elsevier B.V. All rights reserved.
引用
收藏
页码:533 / 541
页数:9
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