Floer homology of cotangent bundles and the loop product
Floer homology of cotangent bundles and the loop product
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余切丛和环积的弗洛尔同调
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发表时间：
2008
期刊：
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通讯作者：
M. Schwarz
中科院分区：
文献类型：
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作者：
Alberto Abbondandolo;M. Schwarz
证明了紧流形M的余切束的花同调上的裤子积对应于M的环空间的奇同调上的查斯-沙利文环积。我们还证明了Pontrjagin产物和Serre纤维的花同源性解释的相关结果。这些技术包括具有跳变Lagrangian边界条件的Cauchy-Riemann算子的Fredholm理论，以及一个取代标准胶合技术的新的协同论证。
We prove that the pair-of-pants product on the Floer homology of the cotangent bundle of a compact manifold M corresponds to the Chas–Sullivan loop product on the singular homology of the loop space of M . We also prove related results concerning the Floer homological interpretation of the Pontrjagin product and of the Serre fibration. The techniques include a Fredholm theory for Cauchy–Riemann operators with jumping Lagrangian boundary conditions of conormal type, and a new cobordism argument replacing the standard gluing technique.