小Seifert L-空间及更多类别的三维辛化问题
The three-dimensional symplectization question for small Seifert L-spaces and further classes
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中文总结 AI 辅助
本文通过构造Liouville配边，解决了小Seifert L-空间等若干三维流形的辛化问题，证明了强可填充性等刚性性质。
中文摘要 AI 辅助
我们解决了若干实例的三维辛化问题。这些实例包括小Seifert纤维化L-空间、Whitehead链环手术L-空间族、S^1×S^2、figure-eight结上的某些手术、Brieskorn球面的显式族，以及这些流形的任意有限连通和。特别地，该结果涵盖了Weeks流形和无穷多个双曲L-空间。主要的辛步骤是从辛化的辛同胚在两个方向上构造Liouville配边。由此得到的强可填充性的保持和单极Floer接触不变量的消失，与Heegaard Floer接触不变量的比较、连通和公式以及紧接触结构的分类结果一起，证明了所述刚性结果。
英文摘要
We solve the three-dimensional symplectization question for several examples. These include small Seifert fibered $L$-spaces, a family of Whitehead-link surgery $L$-spaces, $S^1\times S^2$, certain surgeries on the figure-eight knot, explicit families of Brieskorn spheres, and arbitrary finite connected sums mixing these manifolds. In particular, the result covers the Weeks manifold and infinitely many hyperbolic $L$-spaces. The main symplectic step is to construct Liouville cobordisms in both directions from a symplectomorphism of symplectizations. The resulting preservation of strong fillability and of the vanishing of the monopole Floer contact invariant, together with the comparison with the Heegaard Floer contact invariant, connected-sum formulas, and classification results for tight contact structures, proves the stated rigidity results.
发表机构
- Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo（东京大学宇宙线研究所（WPI））
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