Abstract
Let X be a semialgebraic set in Rn defined by a Boolean combination of atomic formulae of the kind h * 0 where * \in { >, \ge, = }, deg(h) < d, and the number of distinct polynomials h is k. We prove that the sum of Betti numbers of X is less than O(k2d)n.
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Gabrielov, A., Vorobjov, N. Betti Numbers of Semialgebraic Sets Defined by Quantifier-Free Formulae. Discrete Comput Geom 33, 395–401 (2005). https://doi.org/10.1007/s00454-004-1105-7
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DOI: https://doi.org/10.1007/s00454-004-1105-7