Completions and simplicial complexes

Gilles Bertrand (1)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge

In this paper, we first introduce the notion of a completion. Completions are inductive properties which may be expressed in a declarative way and which may be combined. In the sequel of the paper, we show that completions may be used for describing structures or transformations which appear in combinatorial topology. We present two completions, 〈 Cup 〉 and 〈 Cap 〉, in order to define, in an axiomatic way, a remarkable collection of acyclic complexes. We give few basic properties of this collection. Then, we present a theorem which shows the equivalence between this collection and the collection made of all simply contractible simplicial complexes.

Domaines: Traitement des images [eess.IV]; Topologie algébrique [math.AT]

Gilles Bertrand. Completions and simplicial complexes. Discrete Geometry for Computer Imagery, Apr 2011, Nancy, France. pp.129-140, ⟨10.1007/978-3-642-19867-0_11⟩. ⟨hal-00834218⟩