曲弦拓扑与切范畴
Curved String Topology and Tangential Fukaya Categories
摘要：
给定一个单连通流形M，使得其上链代数C^ \star（M）是纯Sullivan dga，本文考虑代数C_ \star（ΩM）的曲变形，并考虑这些代数上的曲模范畴何时成为完全可对偶的.对于简单的流形，如产品的领域，我们能够给出一个明确的标准时，得到的类别的弯曲模是光滑的，适当的和CY，从而产生一个TQFT。我们给弗洛尔理论解释这些理论的射影空间和它们的产品，其中包括定义一个类计数全纯磁盘与规定的切线的除数。
英文摘要：
Given a simply connected manifold M such that its cochain algebra, C^\star(M), is a pure Sullivan dga, this paper considers curved deformations of the algebra C_\star(ΩM) and consider when the category of curved modules over these algebras becomes fully dualizable. For simple manifolds, like products of spheres, we are able to give an explicit criterion for when the resulting category of curved modules is smooth, proper and CY and thus gives rise to a TQFT. We give Floer theoretic interpretations of these theories for projective spaces and their products, which involve defining a Fukaya category which counts holomorphic disks with prescribed tangencies to a divisor.
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