论文标题
福卡亚$ a_ \ infty $ nggebra是不可定向的lagrangian
The Fukaya $A_\infty$ algebra of a non-orientable Lagrangian
论文作者
论文摘要
令$ l \ subset x $为符号歧管$ x $的不一定是相对$ pin $ lagrangian submanifold。我们在$ l $上的微分形式上建立了一个循环Unital Curved $ a_ \ infty $结构，并在本地系统中，由$ l $的本地定位系统给出的本地系统中的值。 $ a_ \ infty $结构的家族是由$ x $相对于$ l $的共同体来参数化的，并且满足类似于Gromov-Witten理论的公理的属性。由于$ L的不可定位性，$ $ j $ - 霍尔光磁盘的评估图可能是$ l $中的边界的，可能是不可定向的。为了解决这个问题，我们使用Orientor演算的最新结果。
Let $L\subset X$ be a not necessarily orientable relatively $Pin$ Lagrangian submanifold in a symplectic manifold $X$. We construct a family of cyclic unital curved $A_\infty$ structures on differential forms on $L$ with values in the local system of graded non-commutative rings given by the tensor algebra of the orientation local system of $L$. The family of $A_\infty$ structures is parameterized by the cohomology of $X$ relative to $L$ and satisfies properties analogous to the axioms of Gromov-Witten theory. On account of the non-orientability of $L,$ the evaluation maps of moduli spaces of $J$-holomorphic disks with boundary in $L$ may not be relatively orientable. To deal with this problem, we use recent results on orientor calculus.
