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Constructive algebraic topology

โœ Scribed by Julio Rubio; Francis Sergeraert

Publisher
Elsevier Science
Year
2002
Tongue
French
Weight
194 KB
Volume
126
Category
Article
ISSN
0007-4497

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โœฆ Synopsis

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.

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