Constructive algebraic topology

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...

Full description

Saved in:
Bibliographic Details
Published in:Bulletin des sciences mathématiques 2002, Vol.126 (5), p.389-412
Main Authors: Rubio, Julio, Sergeraert, Francis
Format: Article
Language:English
Subjects:
Algebraic Topology
Calculus of variations and optimal control
Effective homology
Exact sciences and technology
Functional programming
Homotopy groups
Mathematical analysis
Mathematics
Sciences and techniques of general use
Symbolic computation
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0007-4497
1952-4773
DOI:10.1016/S0007-4497(02)01119-3