论文标题
通过曲曲面脱水率的符号共同体学
Symplectic cohomological rigidity via toric degnerations
论文作者
论文摘要
在本文中，我们研究了符合性的复曲面歧管是否在符合共同体学上是刚性的。在这里，我们说，如果该家族的成员可以通过其积分的共同体学环和其符号形式的共同体类别来区分，那么某些符号歧管的共生共同体学刚性具有。我们展示了如何使用复曲面的变性来产生回答这个问题所需的符号切除术。结果，我们证明，符合性共生型刚性具有具有理性的符号形式的家族，其理性共同体学环对$ \ \ \ althrm {h}^*（（（\ m mathbb {cp}^n;特别是，我们将这种歧管分类为符号切除型。此外，我们证明了任何具有理性符号形式的符号复合形式，其积分的共同体学环是同构的，符合$ \ \ \ mathrm {h} 结构。
In this paper we study whether symplectic toric manifolds are symplectically cohomologically rigid. Here we say that symplectic cohomological rigidity holds for some family of symplectic manifolds if the members of that family can be distinguished by their integral cohomology rings and the cohomology classes of their symplectic forms. We show how toric degenerations can be used to produce the symplectomorphisms necessary to answer this question. As a consequence we prove that symplectic cohomological rigidity holds for the family of symplectic Bott manifolds with rational symplectic form whose rational cohomology ring is isomorphic to $\mathrm{H}^*((\mathbb{CP}^1)^n;\mathbb{Q})$ for some $n$. In particular, we classify such manifolds up to symplectomorphism. Moreover, we prove that any symplectic toric manifold with rational symplectic form whose integral cohomology ring is isomorphic to $\mathrm{H}^*((\mathbb{CP}^1)^n;\mathbb{Z})$ is symplectomorphic to $(\mathbb{CP}^1)^n$ with a product symplectic structure.
