Computing homology groups of simplicial complexes in R3
Computing homology groups of simplicial complexes in R3
复制标题
计算 R3 中单纯复形的同源群
DOI：
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发表时间：
1998
期刊：
影响因子：
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通讯作者：
S. Guha
中科院分区：
文献类型：
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作者：
T. Dey;S. Guha
最近的发展，在分析分子结构和代表固体模型使用单纯复合物，进一步提高了需要计算结构信息的单纯复合物在<bold>R</bold><supscrpt>3</supscrpt>。本文开发了在<supscrpt>R3</supscrpt>中操纵和分析复合物结构所需的基本技术。<bold></bold>
给出了欧氏空间<supscrpt>R3</supscrpt><bold></bold>首先，利用拓扑学的方法分析<bold>了</bold><supscrpt>R3</supscrpt>中的三角剖分三维流形.然后，证明了这些方法实际上可以应用于<supscrpt>R3</supscrpt>中的任意单纯复形，只要模拟了将复形加厚为与之同伦的3-流形的过程，就可以确定复形的结构信息，并解决某些离散问题.<bold></bold>例如，它显示了如何确定同调群，以及具体的表示，其发电机，为一个给定的复杂的<supscrpt>R3</supscrpt><bold></bold>
Recent developments in analyzing molecular structures and representing solid models using simplicial complexes have further enhanced the need for computing structural information about simplicial complexes in <bold>R</bold><supscrpt>3</supscrpt>. This paper develops basic techniques required to manipulate and analyze structures of complexes in <bold>R</bold><supscrpt>3</supscrpt>.
A new approach to analyze simplicial complexes in Euclidean 3-space <bold>R</bold><supscrpt>3</supscrpt> is described. First, methods from topology are used to analyze triangulated 3-manifolds in <bold>R</bold><supscrpt>3</supscrpt>. Then, it is shown that these methods can, in fact, be applied to arbitrary simplicial complexes in <bold>R</bold><supscrpt>3</supscrpt> after (simulating) the process of thickening a complex to a 3-manifold homotopic to it. As a consequence considerable structural information about the complex can be determined and certain discrete problems solved as well. For example, it is shown how to determine homology groups, as well as concrete representations of their generators, for a given complex in <bold>R</bold><supscrpt>3</supscrpt>