New bounds on the
نویسنده
چکیده
A classic result in real algebraic geometry due to Oleinik-Petrovsky, 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 signiicantly better bounds were known on the individual higher Betti numbers. In this paper we prove separate bounds on the diierent Betti numbers of basic semi-algebraic sets, as well as arrangements of algebraic hyper-surfaces. These are the rst results in this direction.
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