Monopole Floer Homology, Eigenform Multiplicities, and the Seifert–Weber Dodecahedral Space
Monopole Floer Homology, Eigenform Multiplicities, and the Seifert–Weber Dodecahedral Space
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DOI：
10.1093/imrn/rnaa310
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发表时间：
2020-03
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影响因子：
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通讯作者：
Francesco Lin;Michael Lipnowski
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文献类型：
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作者：
Francesco Lin;Michael Lipnowski
证明了Seifert-Weber十二面体空间$\mathsf{sw}$是$L$-空间。这一证明建立在我们关于双曲三维流形的Floer同调和谱几何的工作的基础上。由于问题的计算复杂性，我们以前的技术的直接应用遇到了困难。我们利用$\mathsf{sw}$的大对称群、算术和四面体群结构证明了上精确$1$-形式上的小本征值一定有大的重数。
We show that the Seifert-Weber dodecahedral space $\mathsf{SW}$ is an $L$-space. The proof builds on our work relating Floer homology and spectral geometry of hyperbolic three-manifolds. A direct application of our previous techniques runs into difficulties arising from the computational complexity of the problem. We overcome this by exploiting the large symmetry group and the arithmetic and tetrahedral group structure of $\mathsf{SW}$ to prove that small eigenvalues on coexact $1$-forms must have large multiplicity.