论文标题
seidel地图的相互交织关系
An intertwining relation for equivariant Seidel maps
论文作者
论文摘要
Seidel地图是与凸形象征性歧管上的哈密顿圆圈作用相关的两个图，一个关于浮子的共同学，另一个在量子共同体上。我们将其定义扩展到$ s^1 $ - equivariant浮动的同谋，并基于Maulik和Okounkov的建设，将其定义和$ S^1 $ Equivariant量子共同出现。 $ s^1 $ - 用于构建$ s^1 $ equivariant的浮动浮子同胞在应用e earivariant seidel地图后变化（以$ s^1 $ - equivariant量子共生量发生类似的现象）。我们在$ s^1 $ - equivariant量子共同体上显示了Equivariant Seidel地图，与标准Seidel地图不同，与$ S^1 $ - equivariant量子产品相差。我们证明了一个相互交织的关系，该关系完全描述了这种通勤性作为Equivariant Seidel映射的加权版本的失败。我们将探讨如何使用即将到来的论文中的连接来解释这种交织的关系。我们计算了在复杂平面和复杂的投影空间上的旋转动作的模棱两可的seidel图，以及用于旋转重言式线束束在投影空间上的动作。通过这些示例，我们演示了如何使用Equivariant Seidel Maps来计算$ S^1 $ equivariant量子产品和$ s^1 $ - equivariant simphectic simphectic Coomology。
The Seidel maps are two maps associated to a Hamiltonian circle action on a convex symplectic manifold, one on Floer cohomology and one on quantum cohomology. We extend their definitions to $S^1$-equivariant Floer cohomology and $S^1$-equivariant quantum cohomology based on a construction of Maulik and Okounkov. The $S^1$-action used to construct $S^1$-equivariant Floer cohomology changes after applying the equivariant Seidel map (a similar phenomenon occurs for $S^1$-equivariant quantum cohomology). We show the equivariant Seidel map on $S^1$-equivariant quantum cohomology does not commute with the $S^1$-equivariant quantum product, unlike the standard Seidel map. We prove an intertwining relation which completely describes the failure of this commutativity as a weighted version of the equivariant Seidel map. We will explore how this intertwining relationship may be interpreted using connections in an upcoming paper. We compute the equivariant Seidel map for rotation actions on the complex plane and on complex projective space, and for the action which rotates the fibres of the tautological line bundle over projective space. Through these examples, we demonstrate how equivariant Seidel maps may be used to compute the $S^1$-equivariant quantum product and $S^1$-equivariant symplectic cohomology.
