Effective homotopy of fibrations

Original Paper


The well-known effective homology method provides algorithms computing homology groups of spaces. The main idea consists in keeping systematically a deep and subtle connection between the homology of any object and the object itself. Now applying similar ideas to the computation of homotopy groups, we aim to develop a new effective homotopy theory which allows one to determine homotopy groups of spaces. In this work we introduce the notion of a solution for the homotopical problem of a simplicial set, which will be the main definition of our theory, and present an algorithm computing the effective homotopy of a fibration. We also illustrate with examples some applications of our results.


Constructive algebraic topology Homotopy groups Fibrations Spectral sequences 

Mathematics Subject Classification

55Q05 18G30 55T99 68W30 


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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Departamento de Matemáticas y ComputaciónUniversidad de La RiojaLogroñoSpain
  2. 2.Institut FourierUniversité Joseph FourierGrenobleFrance

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