Completions and Simplicial Complexes

  • Gilles Bertrand
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6607)


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.


Completions simplicial complexes collapse simple homotopy combinatorial topology 


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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Gilles Bertrand
    • 1
  1. 1.Laboratoire d’Informatique Gaspard-Monge Equipe A3SIUniversité Paris-Est, ESIEEParisFrance

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