TY - JOUR T1 - Systems of Quadratic Inequalities JF - Proceedings of the London Mathematical Society, Volume 105, Issue 3, September 2012, Pages 622-660 Y1 - 2012 A1 - Andrei A. Agrachev A1 - Antonio Lerario AB - 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. PB - SISSA UR - http://hdl.handle.net/1963/7072 U1 - 7066 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER -