A.A. Agrachev, A. Lerario, Systems of quadratic inequalities

Title: Systems of quadratic inequalities
Authors: A.A. Agrachev, A. Lerario
Journal title: Proceed. London Math. Soc.
Year: 2012
Volume: 105
Pages: 622-660

We present a spectral sequence which efficiently computes Betti numbers of a closed semi-algebraic subset of RP^n defined by a system of quadratic
inequalities and the image of the homology homomorphism induced by the inclusion of this subset in RP^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.