Bordered Floer homology and the branched double cover I
Bordered Floer homology and the branched double cover I
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有边弗洛尔同源性和分支双盖 I
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
D. Thurston
中科院分区：
文献类型：
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作者：
Robert Lipshitz;P. Ozsváth;D. Thurston
给定三球面上的一个连杆，Z. Szab'o和第二作者构造了一个从连杆的Khovanov同调开始，收敛到其分支双盖的Heegaard flower同调的谱序列。本文及其后续的目的是利用有边花同源性来显式计算该谱序列。在这个计算中有两个主要成分：与Dehn扭转相关的过滤双模的显式计算和多边形的配对定理。本文给出了第一个成分，从而得到了从Khovanov同调到Heegaard flower同调的组合谱序列；在续文中，我们证明了这一光谱序列与先前已知的序列一致。
Given a link in the three-sphere, Z. Szab'o and the second author constructed a spectral sequence starting at the Khovanov homology of the link and converging to the Heegaard Floer homology of its branched double-cover. The aim of this paper and its sequel is to explicitly calculate this spectral sequence, using bordered Floer homology. There are two primary ingredients in this computation: an explicit calculation of filtered bimodules associated to Dehn twists and a pairing theorem for polygons. In this paper we give the first ingredient, and so obtain a combinatorial spectral sequence from Khovanov homology to Heegaard Floer homology; in the sequel we show that this spectral sequence agrees with the previously known one.