In a previous paper, under the assumption that the Riemannian metric is special, the author proved some results about the moduli spaces and CW structures arising from Morse theory. By virtue of topological equivalence, this paper extends those results by dropping the assumption on the metric. In particular, we give a strong solution to the following classical question: Does a Morse function on a compact Riemannian manifold give rise to a CW decomposition that is homeomorphic to the manifold?

中文翻译：

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拓扑等价在莫尔斯理论中的应用

在先前的论文中，在假设黎曼度量为特殊假设的情况下，作者证明了有关摩尔斯理论产生的模空间和CW结构的一些结果。通过拓扑等价，本文通过删除度量标准上的假设来扩展这些结果。尤其是，我们为以下经典问题提供了有力的解决方案：紧致黎曼流形上的摩尔斯函数是否会引起流形同胚的CW分解？