Khovanov homology of torus links
Khovanov homology of torus links
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环面链接的霍瓦诺夫同源性
DOI：
10.1016/j.topol.2008.08.004
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发表时间：
2009
影响因子：
0.6
通讯作者：
Marko Stosic
中科院分区：
文献类型：
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作者：
Marko Stosic
本文证明了（2k，2kn）-环面环的Khovanov同调存在一个截断，即（2k，2kn）-环面环的非零同调群的最大同调度为2k 2n.进一步，我们明确地计算了同调度为2k 2n的同调群，并证明了它与M. Khovanov [M. Khovanov，缠结的函子值不变量，代数。托波尔。2（2002）665-741，arXiv：math.QA/0103190]。这给出了M. Khovanov和L. Rozansky在[M.霍瓦诺夫湖Rozansky，A homology theory for links in S2×S1，in preparation。对于任意的n∈N，我们还给出了（3，n）-torus knots同调群秩的一个显式公式。
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 2k2n. Furthermore, we calculate explicitly the homology group in homological degree 2k2n and prove that it coincides with the center of the ring Hkof 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.