On knot Floer width and Turaev genus
On knot Floer width and Turaev genus
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论结Floer宽度和Turaev属
DOI：
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发表时间：
2007
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通讯作者：
Adam M. Lowrance
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作者：
Adam M. Lowrance
对于每一个纽结$K子集S^3$，我们可以将它的纽结Floer同调$hat{HFK}（K）$，一个n阶生成的双阶交换群联系起来。在一般情况下，这些同调群的非零秩位于有限数量的斜率为1的直线上。同调的宽度实质上是两条这样的线之间的最大水平距离。此外，对于$K$的每个图$D$，都有一个相关联的Turaev曲面，并且Turaev亏格是$K$的所有Turaev曲面的最小亏格。我们证明了纽结Floer同调的宽度受Turaev亏格加1的约束。Skein关系的Turaev表面和宽度的复杂的生成结Floer同调的亏格。
To each knot $Ksubset S^3$ one can associated its knot Floer homology $hat{HFK}(K)$, a finitely generated bigraded abelian group. In general, the nonzero ranks of these homology groups lie on a finite number of slope one lines with respect to the bigrading. The width of the homology is, in essence, the largest horizontal distance between two such lines. Also, for each diagram $D$ of $K$ there is an associated Turaev surface, and the Turaev genus is the minimum genus of all Turaev surfaces for $K$. We show that the width of knot Floer homology is bounded by Turaev genus plus one. Skein relations for genus of the Turaev surface and width of a complex that generates knot Floer homology are given.