单有理辛流形中的接触超曲面总是分离的
辛几何
2017-05-17 v4
摘要
我们观察到，在闭辛流形中，带有标记点约束的非零Gromov-Witten不变量对接触超曲面所能表示的同调类施加了限制。作为特例，如果辛流形是单有理的，则接触超曲面必须总是分离的。这去掉了G. Lu的一个结果中多余的假设，从而表明所有嵌入到单有理辛流形中作为接触型超曲面的接触流形都满足Weinstein猜想。我们利用Cieliebak-Mohnke通过Donaldson超曲面定义Gromov-Witten不变量的方法证明了主要结果，因此不需要半正性或虚拟模环。
引用
@article{arxiv.1202.4685,
title = {Contact Hypersurfaces in Uniruled Symplectic Manifolds Always Separate},
author = {Chris Wendl},
journal= {arXiv preprint arXiv:1202.4685},
year = {2017}
}
备注
24 pages, 1 figure; v.3 is a substantial expansion in which the semipositivity condition has been removed by implementing Cieliebak-Mohnke transversality; it also includes a new appendix to explain why the forgetful map in the Cieliebak-Mohnke context is a pseudocycle; v.4 has one short remark added; to appear in J. London Math. Soc