Holomorphic disks and three-manifold invariants: Properties and applications
Holomorphic disks and three-manifold invariants: Properties and applications
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全纯盘和三流形不变量：属性和应用
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
Z. Szabó
中科院分区：
文献类型：
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作者：
P. Ozsváth;Z. Szabó
在[27]中，我们介绍了与具有Spiny结构s∈自旋c (Y)的封闭定向三流形Y相关的HF - (Y,s)、HF∞(Y,s)、HF + (Y, t)、HF（Y,s）和HF red （Y,s）的flower同调理论。本文给出了这些不变量的计算并研究了它们的性质。这些计算表明了一种与Seiberg-Witten理论的推测关系。这些性质包括HF±的欧拉特征与Turaev扭转之间的关系，与最小属问题（Thurston范数）的关系，以及外科精确序列。我们还介绍了这些技术在三流形拓扑中的一些应用。
In [27], we introduced Floer homology theories HF - (Y,s), HF∞(Y,s), HF + (Y, t), HF(Y,s),and HF red (Y, s) associated to closed, oriented three-manifolds Y equipped with a Spiny structures s ∈ Spin c (Y). In the present paper, we give calculations and study the properties of these invariants. The calculations suggest a conjectured relationship with Seiberg-Witten theory. The properties include a relationship between the Euler characteristics of HF ± and Turaev's torsion, a relationship with the minimal genus problem (Thurston norm), and surgery exact sequences. We also include some applications of these techniques to three-manifold topology.