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 $d_2$.

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