离散Morse函数的上升区和下降区
Ascending and descending regions of a discrete Morse function
摘要：
我们提出了一个算法，它产生一个离散的Morse函数类似的Morse-Smale分解的一个光滑流形关于一个光滑的Morse函数的一个规则的细胞复杂的分解。我们的算法相比，类似的现有结果的优点是，它的作品，至少在理论上，在任何维度。实际上，由于更高维度的细胞复合体的大小，存在维度限制。我们证明，该算法是正确的，在这个意义上，它总是产生一个分解成下降和上升区域的关键细胞在有限数量的步骤，并且，经过有限数量的细分，所有的区域是拓扑光盘。算法的效率进行了讨论，并证明了它的性能上的几个例子。
英文摘要：
We present an algorithm which produces a decomposition of a regular cellular complex with a discrete Morse function analogous to the Morse-Smale decomposition of a smooth manifold with respect to a smooth Morse function. The advantage of our algorithm compared to similar existing results is that it works, at least theoretically, in any dimension. Practically, there are dimensional restrictions due to the size of cellular complexes of higher dimensions, though. We prove that the algorithm is correct in the sense that it always produces a decomposition into descending and ascending regions of the critical cells in a finite number of steps, and that, after a finite number of subdivisions, all the regions are topological discs. The efficiency of the algorithm is discussed and its performance on several examples is demonstrated.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
