论文标题
通过离散的摩尔斯
Morse shellings out of discrete Morse functions
论文作者
论文摘要
从拓扑角度来看，有限的简单复合物的摩尔斯炮击是{\ it捏住}操作分解并扩展了经典的壳。我们证明，每个离散的摩尔斯在有限的简单复合物上的功能都会在其第二个barycentric细分上诱导摩尔斯炮击，其临界图块或捏式的柄与一个函数的关键面相对应，从而保留了索引。鉴于在封闭的歧管上的任何光滑的摩尔斯功能，对于在足够多的barycentric细分之后的任何分段线性三角剖分中，也是如此。
From the topological viewpoint, Morse shellings of finite simplicial complexes are {\it pinched} handle decompositions and extend the classical shellings. We prove that every discrete Morse function on a finite simplicial complex induces Morse shellings on its second barycentric subdivision whose critical tiles-or pinched handles-are in oneto-one correspondence with the critical faces of the function, preserving the index. The same holds true, given any smooth Morse function on a closed manifold, for any piecewise-linear triangulation on it after sufficiently many barycentric subdivisions.
