A. Agrachev, A. Lerario, “Systems of quadratic inequalities”, Proceedings of the London Mathematical Society. Third Series, 2012, Volume 105, Issue 3, Pages 622

Abstract: We present a spectral sequence which efficiently computes Betti numbers of a closed semi-algebraic subset of

$\mathbb{R}\mathrm{P}^n$ defined by a system of quadratic inequalities and the image of the homology homomorphism induced by the inclusion of this subset in

$\mathbb{R}\mathrm{P}^n$ . We do not restrict ourselves to the term

$E_2$ of the spectral sequence and give a simple explicit formula for the differential

$d_2$ .

This publication is cited in the following 15 articles:

Mara Belotti, Antonio Lerario, Andrew Newman, “Moduli spaces of geometric graphs”, Algebr. Geom. Topol., 24:4 (2024), 2039
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Vardan Oganesyan, “Zoo of monotone Lagrangians in ${\mathbb {C}}P^n$ ”, Sel. Math. New Ser., 29:5 (2023)
Daniele Mundici, “Deciding Koopman's qualitative probability”, Artificial Intelligence, 299 (2021), 103524
Paul Breiding, Khazhgali Kozhasov, Antonio Lerario, “Random Spectrahedra”, SIAM J. Optim., 29:4 (2019), 2608
G. Khimshiashvili, “Remarks on Quadratic Mappings”, J Math Sci, 237:1 (2019), 135
Saugata Basu, Anthony Rizzie, “Multi-degree Bounds on the Betti Numbers of Real Varieties and Semi-algebraic Sets and Applications”, Discrete Comput Geom, 59:3 (2018), 553
V. A. Krasnov, “On a classical correspondence of real K3 surfaces”, Izv. Math., 82:4 (2018), 662–693
Paul Breiding, Khazhgali Kozhasov, Antonio Lerario, “On the Geometry of the Set of Symmetric Matrices with Repeated Eigenvalues”, Arnold Math J., 4:3-4 (2018), 423
Giorgi Khimshiashvili, Gaiane Panina, Dirk Siersma, Vladimir Zolotov, “Point Charges and Polygonal Linkages”, J Dyn Control Syst, 23:1 (2017), 1
Antonio Lerario, Erik Lundberg, “Gap Probabilities and Betti Numbers of a Random Intersection of Quadrics”, Discrete Comput Geom, 55:2 (2016), 462
A. A. Agrachev, A. Gentile, A. Lerario, “Geodesics and horizontal-path spaces in Carnot Groups”, Geom. Topol., 19:3 (2015), 1569–1630
A. A. Agrachev, “Quadratic cohomology”, Arnold Math. J., 1:1 (2015), 37–58 $https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT={}$
Yan V. Fyodorov, Antonio Lerario, Erik Lundberg, “On the number of connected components of random algebraic hypersurfaces”, Journal of Geometry and Physics, 95 (2015), 1
A. Lerario, “Convex Pencils of Real Quadratic Forms”, Discrete Comput Geom, 2012