The symplectic topology of some rational homology balls
The symplectic topology of some rational homology balls
复制标题
一些有理同调球的辛拓扑
DOI：
10.4171/cmh/327
复制
发表时间：
2012
期刊：
影响因子：
--
通讯作者：
Maksim Maydanskiy
中科院分区：
文献类型：
--
作者：
Yankı Lekili;Maksim Maydanskiy
研究了An Milnor纤维中与Fintushel和Stern的有理同调球微分同构的有限代数商的辛拓扑。我们利用从同调镜像对称出发对An Milnor纤维的Fukaya范畴已有的深刻理解，证明了这些仿射曲面没有闭合的精确拉格朗日子流形。另一方面，我们发现Floer在理论上是必要的单调拉格朗日环面，它被我们在An Milnor纤维中研究的单调环面有限地覆盖。我们得出这些仿射曲面具有不消失的辛上同调。
We study the symplectic topology of some finite algebraic quotients of the An Milnor fibre which are diffeomorphic to the rational homology balls that appear in Fintushel and Stern's rational blowdown construction. We prove that these affine surfaces have no closed exact Lagrangian submanifolds by using the already available and deep understanding of the Fukaya category of the An Milnor fibre coming from homological mirror symmetry. On the other hand, we find Floer theoretically essential monotone Lagrangian tori, finitely covered by the monotone tori which we study in the An Milnor fibre. We conclude that these affine surfaces have non-vanishing symplectic cohomology.