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# Different bounds on the different Betti numbers of semi-algebraic sets

@inproceedings{Basu2001DifferentBO, title={Different bounds on the different Betti numbers of semi-algebraic sets}, author={Saugata Basu}, booktitle={Symposium on Computational Geometry}, year={2001} }

- Published 2001 in Symposium on Computational Geometry
DOI:10.1145/378583.378705

A classic result in real algebraic geometry due to Oleinik-Petrovsky, Thom and Milnor, bounds the {\em 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.
In this paper we prove separate bounds on the different Betti numbers of basic semi-algebraic sets, as well as… CONTINUE READING

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