Abstract
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 ℂ2 transverse to S3 whose slices are non-collarable.
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