Effective homotopy of fibrations

  1. Romero, A. 1
  2. Sergeraert, F. 2
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    GRID grid.119021.a

  2. 2 Joseph Fourier University
    info

    Joseph Fourier University

    Grenoble, Francia

    GRID grid.9621.c

Journal:
Applicable Algebra in Engineering, Communications and Computing

ISSN: 0938-1279

Year of publication: 2012

Volume: 23

Issue: 1-2

Pages: 85-100

Type: Article

Export: RIS
DOI: 10.1007/s00200-012-0168-6 SCOPUS: 2-s2.0-84862023826 WoS: 000304117800006
bar_chart See metrics

Summary

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. Nowapplying 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. © Springer-Verlag 2012.