TY - JOUR
T1 - Homotopically invisible singular curves
JF - Calculus of Variations and Partial Differential Equations
Y1 - 2017
A1 - Andrei A. Agrachev
A1 - Francesco Boarotto
A1 - Antonio Lerario
VL - 56
UR - https://doi.org/10.1007/s00526-017-1203-z
ER -
TY - JOUR
T1 - Homotopy properties of horizontal path spaces and a theorem of Serre in subriemannian geometry
JF - Communications in Analysis and Geometry
Y1 - 2017
A1 - Francesco Boarotto
A1 - Antonio Lerario
PB - International Press of Boston
VL - 25
ER -
TY - THES
T1 - Homology invariants of quadratic maps
Y1 - 2011
A1 - Antonio Lerario
AB - Given 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...
PB - SISSA
UR - http://hdl.handle.net/1963/6245
U1 - 6145
U2 - Mathematics
U3 - Mathematical Physics
U4 - -1
ER -