A note on exact Lagrangian cobordisms with disconnected Legendrian ends

Chantraine, Baptiste

doi:10.1090/S0002-9939-2014-12302-1

A note on exact Lagrangian cobordisms with disconnected Legendrian ends
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by Baptiste Chantraine

Proc. Amer. Math. Soc. 143 (2015), 1325-1331

DOI: https://doi.org/10.1090/S0002-9939-2014-12302-1

Published electronically: October 17, 2014

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Abstract:

We provide in this note two relevant examples of Lagrangian cobordisms. The first one gives an example of two exact Lagrangian submanifolds which cannot be composed in an exact fashion. The second one is an example of an exact Lagrangian cobordism on which each primitive of Liouville form is not constant on the negative end and such that the positive end is a stabilisation whereas the negative end admits augmentations. These examples emphasise a point in the definition of exact Lagrangian cobordisms given by Ekholm, Honda and Kálmán. In order to provide such examples we construct Lagrangian immersions with single double points using an explicit model and interpret such Lagrangians as cobordisms from the Hopf link.

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