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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