New Structures Based on Completions

  • Gilles Bertrand
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7749)


We propose new axioms relative to combinatorial topology. These axioms are settled in the framework of completions which are inductive properties expressed in a declarative way, and that may be combined.

We introduce several completions for describing dyads. A dyad is a pair of complexes which are, in a certain sense, linked by a “relative topology”.

We first give some basic properties of dyads, then we introduce a second set of axioms for relative dendrites. This allows us to establish a theorem which provides a link between dyads and dendrites, a dendrite is an acyclic complex which may be also described by completions. Thanks to a previous result, this result makes clear the relation between dyads, relative dendrites, and complexes which are acyclic in the sense of homology.


Acyclic complexes Combinatorial topology Simplicial Complexes Collapse Completions 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Gilles Bertrand
    • 1
  1. 1.Laboratoire d’Informatique Gaspard-Monge Equipe A3SI, ESIEE ParisUniversité Paris-EstParisFrance

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