Constructive Algebraic Topology

Details Constructive Algebraic Topology Constructive Algebraic Topology

2001-11-22

arxiv.org/abs/math/0111243v1

Mathematics

Algebraic Topology

24 pages, background paper for a plenary talk at the EACA Congress of Tenerife, September 1999

Scientific paper

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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