利用单纯体积计算最大断裂Morse轨迹
Using simplicial volume to count maximally broken Morse trajectories
摘要：
给定一个维数为$n$的闭黎曼流形和一个Morse-Smale函数，负梯度流有100多个$n$ -部分断裂轨线.我们证明了如果流形允许双曲度量，那么$n$ -部分断裂轨线的数目总是至少为双曲体积。证明结合了已知的定理在莫尔斯理论与引理的格罗莫夫关于单纯体积的分层空间。
英文摘要：
Given a closed Riemannian manifold of dimension $n$ and a Morse-Smale function, there are finitely many $n$-part broken trajectories of the negative gradient flow. We show that if the manifold admits a hyperbolic metric, then the number of $n$-part broken trajectories is always at least the hyperbolic volume. The proof combines known theorems in Morse theory with lemmas of Gromov about simplicial volumes of stratified spaces.
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