COMPUTING HOMOLOGY GROUPS OF SIMPLICIAL COMPLEXES IN R-3

Recent developments in analyzing molecular structures and representing solid models using simplicial complexes have further enhanced the nee d for computing structural information about simplicial complexes in R -3. This paper develops basic techniques required to manipulate and an alyze structures of complexes in R-3. A new approach to analyze simpli cial complexes in Euclidean 3-space R-3 is described. First, methods f rom 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 thicken ing a complex to a 3-manifold homotopic to it. As a consequence consid erable structural information about the complex can be determined and certain discrete problems solved as well. For example, it is shown how to determine the homology groups, as well as concrete representations of their generators, for a given complex in R-3.