A sharper estimate on the Betti numbers of sets defined by quadratic inequalities

DOI10.1007/s00454-007-9001-6zbMath1185.14051arXivmath/0610954OpenAlexW2003319152MaRDI QIDQ938303

Michael Kettner, Saugata Basu

Publication date: 19 August 2008

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0610954

zbMATH Keywords

Betti numberssemi-algebraic setsquadratic inequalities

Mathematics Subject Classification ID

Semialgebraic sets and related spaces (14P10) Topology of real algebraic varieties (14P25)

Related Items (7)

Convex pencils of real quadratic forms ⋮ Refined bounds on the number of connected components of sign conditions on a variety ⋮ Geodesic diameter of sets defined by few quadratic equations and inequalities ⋮ Deciding Koopman's qualitative probability ⋮ Multi-degree bounds on the Betti numbers of real varieties and semi-algebraic sets and applications ⋮ Bounding the Betti numbers and computing the Euler-Poincaré characteristic of semi-algebraic sets defined by partly quadratic systems of polynomials ⋮ Computing the Betti numbers of semi-algebraic sets defined by partly quadratic systems of polynomials

Cites Work

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• Efficient algorithm for computing the Euler-Poincaré characteristic of a semi-algebraic set defined by few quadratic inequalities
• Bounding the number of connected components of a real algebraic set
• Topology II. Homotopy and homology. Classical manifolds. Transl. from the Russian
• On bounding the Betti numbers and computing the Euler characteristic of semi-algebraic sets
• On the Betti numbers of semialgebraic sets defined by few quadratic inequalities
• Different bounds on the different Betti numbers of semi-algebraic sets
• Betti numbers of semialgebraic sets defined by quantifier-free formulae
• Polynomial-time computing over quadratic maps i: sampling in real algebraic sets
• Feasibility testing for systems of real quadratic equations
• Topology of quadratic maps and Hessians of smooth maps
• On the Betti numbers of sign conditions
• A Survey of the Hodge Conjecture
• On the Betti Numbers of Real Varieties
• Algorithms in real algebraic geometry

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