Computation of Homology Groups and Generators

Samuel Peltier (1) , Sylvie Alayrangues (1, 2) , Laurent Fuchs (1) , Jacques-Olivier Lachaud (2)

1 SIC - SIGNAL-IMAGE-COMMUNICATION
2 LaBRI - Laboratoire Bordelais de Recherche en Informatique

Topological invariants are extremely useful in many applications related to digital imaging and geometric modelling, and homology is a classical one. We present an algorithm that computes the whole homology of an object of arbitrary dimension: Betti numbers, torsion coefficients and generators. Results on classical shapes in algebraic topology are presented and discussed.

Domaines: Autre [cs.OH]

Samuel Peltier, Sylvie Alayrangues, Laurent Fuchs, Jacques-Olivier Lachaud. Computation of Homology Groups and Generators. Discrete Geometry for Computer Imagery, Apr 2005, Poitiers, France. pp.195--205. ⟨hal-00308012⟩