论文标题
Monopole Floer同源性，特征形式的多重性和Seifert-Weber Deetecahedral空间
Monopole Floer homology, eigenform multiplicities and the Seifert-Weber dodecahedral space
论文作者
论文摘要
我们证明Seifert-Weber DeDeCaheDral Space $ \ Mathsf {sw} $是$ L $ -Space。证明是基于我们的工作，将柔双曲线三序列的浮子同源性和光谱几何形状建立在基础上。我们以前的技术的直接应用是由于问题的计算复杂性而引起的困难。我们通过利用大型对称组以及$ \ mathsf {sw} $的算术和四面体组结构来克服这一点，以证明coecact $ 1 $ - forms上的小特征值必须具有较大的多样性。
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.
