00440nas a2200157 4500008004100000022001400041245004400055210004400099260000800143300000800151490000700159100002500166700002400191700002100215856004600236 2017 eng d a1432-083500aHomotopically invisible singular curves0 aHomotopically invisible singular curves cJul a1050 v561 aAgrachev, Andrei, A.1 aBoarotto, Francesco1 aLerario, Antonio uhttps://doi.org/10.1007/s00526-017-1203-z00569nas a2200133 4500008004100000245009900041210006900140260003400209300001400243490000700257100002400264700002100288856012600309 2017 eng d00aHomotopy properties of horizontal path spaces and a theorem of Serre in subriemannian geometry0 aHomotopy properties of horizontal path spaces and a theorem of S bInternational Press of Boston a269–3010 v251 aBoarotto, Francesco1 aLerario, Antonio uhttps://www.math.sissa.it/publication/homotopy-properties-horizontal-path-spaces-and-theorem-serre-subriemannian-geometry01189nas a2200109 4500008004100000245004200041210004200083260001000125520088700135100002101022856003601043 2011 en d00aHomology invariants of quadratic maps0 aHomology invariants of quadratic maps bSISSA3 aGiven a real projective algebraic set X we could hope that the equations describing it can give some information on its topology, e.g. on the number of its connected components. Unfortunately in the general case this hope is too vague and there is no direct way to extract such information from the algebraic description of X: Even the problem to decide whether X is empty or not is far from an easy visualization and requires some complicated algebraic machinery. A fi rst step observation is that as long as we are interested only in the topology of X, we can replace, using some Veronese embedding, the original ambient space with a much bigger RPn and assume that X is cut by quadratic equations. The price for this is the increase of the number of equations de ning our set; the advantage is that quadratic polynomials are easier to handle and our hope becomes more concrete...1 aLerario, Antonio uhttp://hdl.handle.net/1963/6245