Constructive Algebraic Topology

  1. Rubio, J. 1
  2. Sergeraert, F. 2
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

  2. 2 Institut Fourier
    info

    Institut Fourier

    Saint-Martin-d’Hères, Francia

    ROR https://ror.org/05rwrfh97

Revista:
Bulletin des Sciences Mathematiques

ISSN: 0007-4497

Any de publicació: 2002

Volum: 126

Número: 5

Pàgines: 389-412

Tipus: Article

DOI: 10.1016/S0007-4497(02)01119-3 SCOPUS: 2-s2.0-0036270808 WoS: WOS:000176707300004 arXiv: 0111243 GOOGLE SCHOLAR lock_openAccés obert editor

Altres publicacions en: Bulletin des Sciences Mathematiques

Repositori institucional: lock_openAccés obert Editor

Resum

The classical "computation" methods in Algebraic Topology most often work by means of highly infinite objects and in fact are not constructive. Typical examples are shown to describe the nature of the problem. The Rubio-Sergeraert solution for Constructive Algebraic Topology is recalled. This is not only a theoretical solution: the concrete computer program Kenzo has been written down which precisely follows this method. This program has been used in various cases, opening new research subjects and producing in several cases significant results unreachable by hand. In particular the Kenzo program can compute the first homotopy groups of a simply connected arbitrary simplicial set. © 2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved.