Different Bounds on the Different Betti Numbers of Semi-Algebraic Sets

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机构：
[1] School of Mathematics and College of Computing,
[2] Georgia Institute of Technology,undefined
[3] Atlanta,undefined
[4] GA 30332,undefined
[5] USA saugata@math.gatech.edu,undefined
来源：
Discrete & Computational Geometry | 2003年 / 30卷
关键词：
Algebraic Geometry; Classic Result; Betti Number; Topological Complexity; Good Bound;
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摘要：
Abstract. A classic result in real algebraic geometry due to Oleinik—Petrovskii, Thom and Milnor, bounds the topological complexity (the sum of the Betti numbers) of basic semi-algebraic sets. This bound is tight as one can construct examples having that many connected components. However, till now no significantly better bounds were known on the individual higher Betti numbers.
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页码：65 / 85
页数：20
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