Floer Homology and Mirror Symmetry II
Floer Homology and Mirror Symmetry II
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DOI：
10.2969/aspm/03410031
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
K. Fukaya
中科院分区：
文献类型：
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作者：
K. Fukaya
这是解释Floer同调在镜像对称性和D-膜中的应用的系列文章的第二部分。本文独立于第一部分[Fu9]。我们将把$A_{INFTY}$范畴与辛流形联系起来。这是以前的[Fu1]、[Fu4]的改进版本，其中有一些缺陷。这一更正是基于与Oh，Ohta，Ono联合撰写的一本书[Fooo]。在纠正缺陷的同时，我们发现了与镜面对称性有关的各种有趣的新现象。本文还讨论了$A_(Inty)$范畴的同调代数。这篇文章是一篇调查文章。因此，这里写的大部分材料都是对结果的微小修改，有些人已经知道了。然而，很难找到他们的参考资料。
This is the second part of a series of articles explaining applications of Floer homology to mirror symmetry and D-brane. This article is independent of part I [Fu9]. We will associate an $A_{\infty}$ category to a symplectic manifold. This is an improved version of previous ones [Fu1], [Fu4] in which there were some flaw. The correction is based on a book [FOOO] written jointly with Oh, Ohta, Ono. While correcting the flaw, we find various interesting new phenomena which are related to mirror symmetry. We also discuss homological algebra of $A_{\infty}$ category in this article. This article is a survey article. So most of the material written here are minor modifications of the results which are already known to somebody. However it is rather hard to find a reference of them.