Do uniruled six-manifolds contain Sol Lagrangian submanifolds? - Institut Camille Jordan Accéder directement au contenu
Article Dans Une Revue International Mathematics Research Notices Année : 2012

Do uniruled six-manifolds contain Sol Lagrangian submanifolds?

Résumé

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 its image contains the boundary of a symplectic disc with vanishing Maslov index. This prevents such a Lagrangian submanifold to be monotone, for instance the real locus of a smooth real Fano manifold. It also prevents any Sol manifold to be in the real locus of an orientable real Del Pezzo fibration over a curve, confirming an expectation of J. Kollár. Finally, it constraints Hamiltonian diffeomorphisms of uniruled symplectic four-manifolds.
Fichier principal
Vignette du fichier
solmanifolds.pdf (294.37 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00447962 , version 1 (17-01-2010)

Identifiants

Citer

Frédéric Mangolte, Jean-Yves Welschinger. Do uniruled six-manifolds contain Sol Lagrangian submanifolds?. International Mathematics Research Notices, 2012, 2012, pp.1569-1602. ⟨10.1093/imrn/rnr063⟩. ⟨hal-00447962⟩
313 Consultations
149 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More