53 citations · 222 across the 25 of their papers we have counts for
9 papers · 1 filter
Lower estimates for the expected Betti numbers of random real hypersurfaces
Damien Gayet, Jean-Yves Welschinger
We estimate from below the expected Betti numbers of real hypersurfaces taken at random in a smooth real projective n-dimensional manifold. These random hypersurfaces are chosen in…
Open Gromov-Witten invariants in dimension six
Jean-Yves Welschinger
Let be a closed orientable Lagrangian submanifold of a closed symplectic six-manifold . We assume that the first homology group with coefficients in a com…
Open Gromov-Witten invariants in dimension four
Jean-Yves Welschinger
Given a closed orientable Lagrangian surface L in a closed symplectic four-manifold X together with a relative homology class d in H_2 (X, L; Z) with vanishing boundary in H_1 (L;…
Do uniruled six-manifolds contain Sol Lagrangian submanifolds?
Frédéric Mangolte, Jean-Yves Welschinger
We prove using symplectic field theory that if the suspension of a hyperbolic diffeomorphism of the two-torus Lagrangian embeds in a closed uniruled symplectic six-manifold, then i…
Associahedral categories, particles and Morse functor
Jean-Yves Welschinger
Every smooth manifold contains particles which propagate. These form objects and morphisms of a category equipped with a functor to the category of Abelian groups, turning this int…
Open strings, Lagrangian conductors and Floer functor
Jean-Yves Welschinger
We introduce a contravariant functor, called Floer functor, from the category of Lagrangian conductors of a symplectic manifold to the homotopy category of bounded chain complexes…
Effective classes and Lagrangian tori in symplectic four-manifolds
Jean-Yves Welschinger
An effective class in a closed symplectic four-manifold is a two-dimensional homology class which is realized by a -holomorphic cycle for every tamed almost complex str…
Towards relative invariants of real symplectic 4-manifolds
Jean-Yves Welschinger
Let be a real symplectic 4-manifold with real part . Let be a smooth curve such that . We construct invariants un…
Invariants of real symplectic 4-manifolds out of reducible and cuspidal curves
Jean-Yves Welschinger
We construct invariants under deformation of real symplectic 4-manifolds. These invariants are obtained by counting three different kinds of real rational J-holomorphic curves whic…