We give a simple algorithm for the computational determination of the (co)homology groups of a compact polyhedron (and, in particular, of a triangulated manifold) starting from a combinatorial representation of it by edge-colored graphs. Several examples illustrate the validity of our algorithm in particular cases. Finally, we obtain a partial catalogue of the (co)homological characters for a family of closed connected orientable 3-manifolds, dependent on three positive integers and a permutation.
A graph theoretical algorithm for computing the (co)homology of polyhedra / Cavicchioli, Alberto; Meschiari, Mauro; Spaggiari, Fulvia. - In: ITALIAN JOURNAL OF PURE AND APPLIED MATHEMATICS. - ISSN 1126-8042. - STAMPA. - 2:(1997), pp. 19-36.
A graph theoretical algorithm for computing the (co)homology of polyhedra
CAVICCHIOLI, Alberto;MESCHIARI, Mauro;SPAGGIARI, Fulvia
1997
Abstract
We give a simple algorithm for the computational determination of the (co)homology groups of a compact polyhedron (and, in particular, of a triangulated manifold) starting from a combinatorial representation of it by edge-colored graphs. Several examples illustrate the validity of our algorithm in particular cases. Finally, we obtain a partial catalogue of the (co)homological characters for a family of closed connected orientable 3-manifolds, dependent on three positive integers and a permutation.
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