Algorithmic Semi-algebraic Geometry and Topology -- Recent Progress and Open Problems

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We give a survey of algorithms for computing topological invariants of semi-algebraic sets with special emphasis on the more recent developments in designing algorithms for computing the Betti numbers of semi-algebraic sets. Aside from describing these results, we discuss briefly the background as well as the importance of these problems, and also describe the main tools from algorithmic semi-algebraic geometry, as well as algebraic topology, which make these advances possible. We end with a list of open problems.
Survey article, 74 pages, 15 figures. Final revision. This version will appear in the AMS Contemporary Math. Series: Proceedings of the Summer Research Conference on Discrete and Computational Geometry, Snowbird, Utah (June, 2006). J.E. Goodman, J. Pach, R. Pollack Eds

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Geometric Topology, Computational Complexity, Computational Geometry, Algebraic Geometry, Algebraic Topology, 14P10, 14P25 (Primary) 68W30 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/137976

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0708.2854
 http://arxiv.org/abs/0708.2854

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arXiv