Dimensionally-reduced sutured Floer homology as a string homology
Dimensionally-reduced sutured Floer homology as a string homology
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降维缝合 Floer 同源作为弦同源
DOI：
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发表时间：
2012
期刊：
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通讯作者：
E. Schoenfeld
中科院分区：
文献类型：
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作者：
Daniel V. Mathews;E. Schoenfeld
我们证明了形式为.D 2 S 1 ;F S 1 /的缝合3-流形的缝合Floer同调可以表示为弦型复形的同调，由.D 2 ;F/上的某些曲线集生成，并具有通过求解交叉给出的微分。我们也给出了一些概括的同构，计算“帽子”和“无穷”版本的这个字符串同源。除了给有趣的基本事实代数的曲线曲面，这些同构的启发，并建立进一步，连接之间的不变量从弗洛尔同源性和字符串拓扑。
We show that the sutured Floer homology of a sutured 3‐manifold of the form .D 2 S 1 ;F S 1 / can be expressed as the homology of a string-type complex, generated by certain sets of curves on .D 2 ;F/ and with a differential given by resolving crossings. We also give some generalisations of this isomorphism, computing “hat” and “infinity” versions of this string homology. In addition to giving interesting elementary facts about the algebra of curves on surfaces, these isomorphisms are inspired by, and establish further, connections between invariants from Floer homology and string topology.