@article {2012, title = {Systems of Quadratic Inequalities}, journal = {Proceedings of the London Mathematical Society, Volume 105, Issue 3, September 2012, Pages 622-660}, number = {arXiv:1012.5731;}, year = {2012}, publisher = {SISSA}, 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.}, doi = {DOI: 10.1112/plms/pds010}, url = {http://hdl.handle.net/1963/7072}, author = {Andrei A. Agrachev and Antonio Lerario} }