Some non-collarable slices of Lagrangian surfaces

Baptiste Chantraine (1)

1 LMJL - Laboratoire de Mathématiques Jean Leray

In this note we define the notion of collarable slices of Lagrangian submanifolds. These are slices of Lagrangian submanifolds which can be isotoped through Lagrangian submanifolds to a cylinder over a Legendrian embedding near a contact hypersurface. Such a notion arises naturally when studying intersections of Lagrangian submanifolds with contact hypersurfaces. We then give two explicit examples of Lagrangian disks in C 2 transverse to S 3 whose slices are non-collarable.

Domaines: Géométrie symplectique [math.SG]

Baptiste Chantraine. Some non-collarable slices of Lagrangian surfaces. Bulletin of the London Mathematical Society, 2012, 44 (5), http://blms.oxfordjournals.org/content/44/5/981. ⟨10.1112/blms/bds026⟩. ⟨hal-01135643⟩