On the number of topological types occurring in a parametrized family of arrangements, preprint, available at [arXiv:0704.0295

On the number of topological types occurring in a parametrized family of arrangements, preprint, available at [arXiv:0704.0295 (0)

by S Basu

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Algorithmic Semi-algebraic Geometry and Topology – Recent Progress and Open Problems (expository article, 73 pages), to appear

by Saugata Basu - in AMS Contemporary Mathematics Series, Proceedings the Summer Research Conference on Discrete and Computational Geometry – Twenty years later, Snowbird , 2006

"... Abstract. In this lecture we introduce semi-algebraic sets, Tarski-Seidenberg principle, give basic definitions of homology and co-homology groups of semi-algebraic sets, and state certain quantitative results which give tight bounds on the ranks of these groups. We also state several ..."

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Abstract. In this lecture we introduce semi-algebraic sets, Tarski-Seidenberg principle, give basic definitions of homology and co-homology groups of semi-algebraic sets, and state certain quantitative results which give tight bounds on the ranks of these groups. We also state several

Contemporary Mathematics Algorithmic Semi-algebraic Geometry and Topology – Recent Progress and Open Problems

by Saugata Basu

"... Abstract. 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 semialgebraic sets. Aside from describing these results, we discuss briefly the backgr ..."

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Abstract. 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 semialgebraic 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.