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Abstract: In this paper we give a new bound on the sum of the Betti numbers of semi-algebraic sets. This extends a well-known bound due to Oleinik and Petrovsky [19], Thom [23] and Milnor [18]. In separate papers they proved that the sum of the Betti numbers of a semi-algebraic set S ae R defined by P 1 0; : : : ; P s 0; deg(P i ) d; 1 i s; is bounded by (O(sd)) : Given a semialgebraic set S ae R defined as the intersection of a real variety, Q = 0; deg(Q) d; whose real dimension is k ... (Update)
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BibTeX entry: (Update)
Saugata Basu. On bounding the Betti numbers and computing the Euler characteristic of semi-algebraic sets. In Proc. 28th Annu. ACM Sympos. Theory Comput., pages 408--417, 1996. http://citeseer.ist.psu.edu/basu96bounding.html More
@inproceedings{ basu96bounding,
author = "Saugata Basu",
title = "On bounding the {Betti} numbers and computing the {Euler} characteristic of semi-algebraic sets",
pages = "408--417",
year = "1996",
url = "citeseer.ist.psu.edu/basu96bounding.html" }
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