Computing homology groups of simplicial complexes in R 3
Tamal K. Dey, Sumanta Guha · Journal of the ACM · 1998
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 R 3 . This paper develops basic techniques required to manipulate and analyze structures of complexes in R 3 . A new approach to analyze simplicial complexes in Euclidean 3-space R 3 is described. First, methods from topology are used to analyze triangulated 3-manifolds in R 3 . Then, it is shown that these methods can, in fact, be applied to arbitrary simplicial complexes in R 3 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 R 3