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

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dc.creatorBasu, Saugata
dc.date2007-08-21
dc.date2007-09-15
dc.date.accessioned2026-07-07T08:29:33Z
dc.date.available2026-07-07T08:29:33Z
dc.descriptionWe 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.
dc.descriptionSurvey 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
dc.identifierhttps://arxiv.org/abs/0708.2854
dc.identifierhttp://arxiv.org/abs/0708.2854
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/137976
dc.subjectGeometric Topology
dc.subjectComputational Complexity
dc.subjectComputational Geometry
dc.subjectAlgebraic Geometry
dc.subjectAlgebraic Topology
dc.subject14P10, 14P25 (Primary) 68W30 (Secondary)
dc.titleAlgorithmic Semi-algebraic Geometry and Topology -- Recent Progress and Open Problems
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