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摘要翻译：
本文的主要结果是：每个闭Hamilton S^1流形是不变的，即它有一个非零Gromov-Witten不变量，其约束是一个点。证明采用了M的小量子同调中哈密顿群的\pi_1的Seidel表示，以及Hu、Li和Ruan最近提出的blow-up技术。它更普遍地应用于具有一个具有非退化固定极大值的哈密顿辛明天圈的流形。对Hofer几何学的一些结果进行了探讨。一个附录讨论了无圈流形的量子同调环的结构。
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英文标题：
《Hamiltonian S^1 manifolds are uniruled》
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作者：
Dusa McDuff
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最新提交年份：
2009
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分类信息：
一级分类：Mathematics 数学
二级分类：Symplectic Geometry 辛几何
分类描述：Hamiltonian systems, symplectic flows, classical integrable systems
哈密顿系统，辛流，经典可积系统
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一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
The main result of this note is that every closed Hamiltonian S^1 manifold is uniruled, i.e. it has a nonzero Gromov--Witten invariant one of whose constraints is a point. The proof uses the Seidel representation of \pi_1 of the Hamiltonian group in the small quantum homology of M as well as the blow up technique recently introduced by Hu, Li and Ruan. It applies more generally to manifolds that have a loop of Hamiltonian symplectomorphisms with a nondegenerate fixed maximum. Some consequences for Hofer geometry are explored. An appendix discusses the structure of the quantum homology ring of uniruled manifolds.
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PDF链接：
https://arxiv.org/pdf/0706.0675
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