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arXiv · 1108.2969

Some non-collarable slices of Lagrangian surfaces

Baptiste Chantraine
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Abstract

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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Baptiste Chantraine. 2012-01-16. Some non-collarable slices of Lagrangian surfaces. https://doi.org/10.1112/blms%2Fbds026

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