Constructive Algebraic Topology
- Rubio, J. 1
- Sergeraert, F. 2
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1
Universidad de La Rioja
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2
Institut Fourier
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ISSN: 0007-4497
Año de publicación: 2002
Volumen: 126
Número: 5
Páginas: 389-412
Tipo: Artículo
Otras publicaciones en: Bulletin des Sciences Mathematiques
Resumen
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.