On the Khovanov and knot Floer homologies of quasi-alternating links
On the Khovanov and knot Floer homologies of quasi-alternating links
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准交替链的Khovanov和Knot Floer同调
DOI：
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发表时间：
2007
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通讯作者：
P. Ozsváth
中科院分区：
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作者：
Ciprian Manolescu;P. Ozsváth
准交替链接是交替链接的自然推广。在本文中，我们证明了拟交替链接是“同调薄”的Khovanov同调和结Floer同调。特别地，它们的双阶同调群由链接的签名以及相应同调的欧拉特征（即Jones或亚历山大多项式）确定。证明使用的确切三角形有关的同源性的一个链接的同源性的两个决议在一个交叉。
Quasi-alternating links are a natural generalization of alternating links. In this paper, we show that quasi-alternating links are "homologically thin" for both Khovanov homology and knot Floer homology. In particular, their bigraded homology groups are determined by the signature of the link, together with the Euler characteristic of the respective homology (i.e. the Jones or the Alexander polynomial). The proofs use the exact triangles relating the homology of a link with the homologies of its two resolutions at a crossing.