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Completions and simplicial complexes

Abstract : 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 in order to define, in an axiomatic way, a remarkable collection of acyclic complexes. We give some basic properties of this collection. Then, we present a theorem which shows the equivalence between this collection and the collection made of all complexes that are acyclic in the sense of homology theory.
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https://hal-upec-upem.archives-ouvertes.fr/hal-00761162
Contributor : Gilles Bertrand <>
Submitted on : Wednesday, December 5, 2012 - 9:28:12 AM
Last modification on : Wednesday, February 26, 2020 - 7:06:06 PM
Long-term archiving on: : Wednesday, March 6, 2013 - 4:55:45 PM

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  • HAL Id : hal-00761162, version 1

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Gilles Bertrand. Completions and simplicial complexes. [Research Report] LIGM. 2012. ⟨hal-00761162⟩

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