通过实测层叠（Measured Laminations）计算本质曲面的增长率
Growth Rate of Essential Surfaces via Measured Laminations
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中文总结 AI 辅助
该研究在哈肯3-流形中建立了$\text{ML}$及$\text{ML}_0$维数与正规曲面的关联，进而推导了特定双曲3-流形中高欧拉特征闭定向本质曲面数量的渐近增长规律。
中文摘要 AI 辅助
我们证明了在任意哈肯3-流形M中，$\boldsymbol{\text{ML}}(M)$和$\boldsymbol{\text{ML}}_0(M)$的维数可通过正规曲面计算；作为推论，我们证明：当闭定向双曲3-流形M满足$H_2(M,\boldsymbol{\text{Z}}/2\boldsymbol{\text{Z}})=0$时，欧拉特征至少为$-2n$的闭定向本质曲面数量渐近于$n^{\boldsymbol{\text{dim}}\boldsymbol{\text{ML}}_0(M)}$。
英文摘要
We show that in any Haken 3-manifold $M$, the dimensions of $\mathcal{ML}(M)$ and $\mathcal{ML}_0(M)$ can be calculated using normal surfaces. As a corollary, we prove the number of closed orientable essential surfaces of Euler characteristic at least $-2n$ in a closed orientable hyperbolic 3-manifold with $H_2(M,\mathbb{Z}/2\mathbb{Z}) = 0$ is asymptotic to $n^{\dim \mathcal{ML}_0(M)}$.
