Some non-collarable slices of Lagrangian surfaces

Details Some non-collarable slices of Lagrangian surfaces Some non-collarable slices of Lagrangian surfaces

2011-08-15

arxiv.org/abs/1108.2969v2

Mathematics

Symplectic Geometry

7 pages, 5 figures. Minor corrections. To appear in the Bulletin of the London Mathematical Society (published version will be

Scientific paper

In this note we define the notion of collarable slices of Lagrangian submanifolds. Those 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 $\mathbb{C}^2$ transverse to $S^3$ whose slices are non-collarable.

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