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Symplectic fillings and cobordisms of lens spaces
Transactions of the American Mathematical Society ( IF 1.2 ) Pub Date : 2021-09-15 , DOI: 10.1090/tran/8474
John Etnyre , Agniva Roy

Abstract:We complete the classification of symplectic fillings of tight contact structures on lens spaces. In particular, we show that any symplectic filling $X$ of a virtually overtwisted contact structure on $L(p,q)$ has another symplectic structure that fills the universally tight contact structure on $L(p,q)$. Moreover, we show that the Stein filling of $L(p,q)$ with maximal second homology is given by the plumbing of disk bundles. We also consider the question of constructing symplectic cobordisms between lens spaces and report some partial results.


中文翻译:

晶状体空间的辛填充和坐标系

摘要:我们完成了晶状体空间上紧密接触结构辛填充物的分类。特别是,我们证明了 $L(p,q)$ 上几乎过度扭曲的接触结构的任何辛填充 $X$ 都有另一个辛结构填充 $L(p,q)$ 上的普遍紧接触结构。此外,我们表明具有最大第二同源性的 $L(p,q)$ 的 Stein 填充是由磁盘束的管道给出的。我们还考虑了在透镜空间之间构建辛协边的问题,并报告了一些部分结果。
更新日期:2021-11-09
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