Structure on the top homology and related algorithms

We explore the special structure of top-dimensional homology any compact triangulable space X dimension d. Since there are no (d+1)-dimensional cells, top equals cycles and is thus a free abelian group. There obvious basis, but we show that canonical embedding into group which has natural basis up to signs. This an invariant homeomorphism. circumstance gives (orientable) matroid, where in sense matroids correspond homology. adds novel topological literature. apply this matroid on give polynomial-time algorithm for construction (over Z coefficients).