A remark on the geography problem in Heegaard Floer homology
A remark on the geography problem in Heegaard Floer homology
复制标题
对Heegaard Floer同调中地理问题的评述
DOI：
10.1090/pspum/102/08
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
Lidman, Tye
中科院分区：
文献类型：
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作者：
Hanselman, Jonathan;Kutluhan, Çagatay;Lidman, Tye
我们给Heegaard Floer同调中出现的模结构提出了新的障碍。作为一个推论，我们的特点可能出现的Heegaard Floer同调的整数同调球一维减少Floer同调的模块。到了绝对等级变化，只有两个。我们使用这个推论表明，链复杂描绘Ozsv\'ath，Stipsicz和Szab\' o认为，没有代数障碍存在的nodes与trivialinvariant和non-trivialinvariant不能实现为结Floer复杂的结。
We give new obstructions to the module structures arising in Heegaard Floer homology. As a corollary, we characterize the possible modules arising as the Heegaard Floer homology of an integer homology sphere with one-dimensional reduced Floer homology. Up to absolute grading shifts, there are only two. We use this corollary to show that the chain complex depicted by Ozsv\'ath, Stipsicz, and Szab\'o to argue that there is no algebraic obstruction to the existence of knots with trivialinvariant and non-trivialinvariant cannot be realized as the knot Floer complex of a knot.