Constructive algebraic topology |
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Authors: | Julio RubioFrancis Sergeraert |
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Affiliation: | a Depto Mat. y Comp., Univ. de la Rioja, 26004 Logroño, La Rioja, Espagne b Institut Fourier, Univ. Grenoble I, Lab. Assoc. CNRS, B.P. 74, 38402, St. Martin D'Heres cedex, France |
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Abstract: | 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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Keywords: | Algebraic topology Effective homology Homotopy groups Functional programming Symbolic computation |
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