$U$-action on perturbed Heegaard–Floer homology
$U$-action on perturbed Heegaard–Floer homology
复制标题
对扰动 Heegaard-Floer 同源性的 $U$ 行动
DOI：
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发表时间：
2012
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影响因子：
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通讯作者：
Zhongtao Wu
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文献类型：
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作者：
Zhongtao Wu
本文有两个目的。首先，作为“一些纤维三流形的扰动Floer同调”的继续，我们用类似的方法计算了第二高自旋c-结构中一些特殊的纤维三流形的扰动Hf^+，包括沿单条非分离曲线和沿一对横向曲线的Dehn扭环。其次，我们建立了扰动Heegaard-Floer同调的一个伴随不等式，它表明了三维流形上的U-作用量与三维流形的瑟斯顿范数之间的潜在联系。作为应用，我们发现上述纤维三维流形的扰动HF^+上的U作用量是微不足道的。
This paper has two purposes. First, as a continuation of "Perturbed Floer homology of some fibered three manifolds," we apply a similar method to compute the perturbed HF^+ for some special classes of fibered three-manifolds in the second highest spin^c_- structures, including the mapping tori of Dehn twists along a single non-separating curve and along a transverse pair of curves. Second, we establish an adjunction inequality for the perturbed Heegaard Floer homology, which indicates a potential connection between the U-action on the homology group and the Thurston norm of a three-manifold. As an application, we find the U-action on the perturbed HF^+ of the above classes of fibered three-manifolds is trivial.