Dima Grigoriev, Nicolai Vorobjov
Published 2017-09-25Version 1
We prove upper bounds on the sum of Betti numbers of tropical prevarieties in dense and sparse settings. In the dense setting the bound is in terms of the volume of Minkowski sum of Newton polytopes of defining tropical polynomials, or, alternatively, via the maximal degree of these polynomials. In sparse setting, the bound involves the number of the monomials.
Bounding the Betti numbers of real hypersurfaces near the tropical limit
Approximation of definable sets by compact families, and upper bounds on homotopy and homology
Elimination theory and Newton polytopes
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