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

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 $$d_2$$.