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Skein relations for tangle Floer homology
Quantum Topology ( IF 1.0 ) Pub Date : 2020-02-24 , DOI: 10.4171/qt/134
Ina Petkova 1 , C.-M. Michael Wong 2
Affiliation  

In a previous paper, V\'ertesi and the first author used grid-like Heegaard diagrams to define tangle Floer homology, which associates to a tangle $T$ a differential graded bimodule $\widetilde{\mathrm{CT}} (T)$. If $L$ is obtained by gluing together $T_1, \dotsc, T_m$, then the knot Floer homology $\widehat{\mathrm{HFK}}(L)$ of $L$ can be recovered from $\widetilde{\mathrm{CT}} (T_1), \dotsc, \widetilde{\mathrm{CT}} (T_m)$. In the present paper, we prove combinatorially that tangle Floer homology satisfies unoriented and oriented skein relations, generalizing the skein exact triangles for knot Floer homology.

中文翻译:

缠结 Floer 同源性的绞线关系

在之前的一篇论文中,V\'ertesi 和第一作者使用类似网格的 Heegaard 图来定义缠结 Floer 同源性,该同源性将一个缠结 $T$ 关联到一个微分分级双模 $\widetilde{\mathrm{CT}} (T) $. 如果将$T_1、\dotsc、T_m$粘合在一起得到$L$,则可以从$\widetilde{\恢复$L$的结Floer同源性$\widehat{\mathrm{HFK}}(L)$ mathrm{CT}} (T_1), \dotsc, \widetilde{\mathrm{CT}} (T_m)$。在本文中,我们组合证明了缠结 Floer 同源性满足无向和有向绞线关系,推广了结 Floer 同源性的绞线精确三角形。
更新日期:2020-02-24
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