Computation of homology groups and generators

S. Peltier, S. Alayrangues, L. Fuchs, Jacques-Olivier Lachaud
January, 2005
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Abstract

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.

Type
Conference paper
Publication
Proc. Int. Conf. Discrete Geometry for Computer Imagery (DGCI'2005), Poitiers, France, volume 3429 of Lecture Notes in Computer Science, pp 195–205, 2005. Springer
digital topology combinatorial topology topological invariants homology computation homology generators Smith Normal form simplicial homology nD
Jacques-Olivier Lachaud
Jacques-Olivier Lachaud
Professor of Computer Science

My research interests include digital geometry, geometry processing, image analysis, variational models and discrete calculus.