论文标题
循环开放式地图，U-Connections和R-Matrices
The cyclic open-closed map, u-connections and R-matrices
论文作者
论文摘要
本文考虑（负）环状开放式地图$ \ MATHCAL {OC}^{ - } $，它映射了Symplectic歧管的Fukaya类别的周期性同源性，以绘制其$ S^1 $ equivariant量子同学。我们证明（在简化的技术假设下），该地图尊重e earivariant参数方向的各自的自然连接。在单调设置中，这使我们能够得出结论，$ \ MATHCAL {OC}^{ - } $通过量子杯产品的特征值与Hukuhara-Levelt-levelt-Turrittin的量子同类素的量子类别相结合了福卡亚类别的分解。我们还解释了我们的结果如何与半imple辅助同谋领域理论的Givental-Teleman分类相关：特别是，在半神经案例中，R-Matrix与$ \ Mathcal {oc}^{ - } $如何相关；我们还考虑了非偏simimple案例。
This paper considers the (negative) cyclic open-closed map $\mathcal{OC}^{-}$, which maps the cyclic homology of the Fukaya category of a symplectic manifold to its $S^1$-equivariant quantum cohomology. We prove (under simplifying technical hypotheses) that this map respects the respective natural connections in the direction of the equivariant parameter. In the monotone setting this allows us to conclude that $\mathcal{OC}^{-}$ intertwines the decomposition of the Fukaya category by eigenvalues of quantum cup product with the first Chern class, with the Hukuhara-Levelt-Turrittin decomposition of the quantum cohomology. We also explain how our results relate to the Givental-Teleman classification of semisimple cohomological field theories: in particular, how the R-matrix is related to $\mathcal{OC}^{-}$ in the semisimple case; we also consider the non-semisimple case.
