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A note on exact Lagrangian cobordisms with disconnected Legendrian ends


Author: Baptiste Chantraine
Journal: Proc. Amer. Math. Soc. 143 (2015), 1325-1331
MSC (2010): Primary 57R17; Secondary 53D42, 57M50
DOI: https://doi.org/10.1090/S0002-9939-2014-12302-1
Published electronically: October 17, 2014
MathSciNet review: 3293745
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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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Additional Information

Baptiste Chantraine
Affiliation: Laboratoire de Mathématiques Jean Leray, 2 rue de la Houssinire, BP 92208, F-44322 Nantes Cedex 3, France
Email: baptiste.chantraine@univ-nantes.fr

DOI: https://doi.org/10.1090/S0002-9939-2014-12302-1
Received by editor(s): January 29, 2013
Received by editor(s) in revised form: July 2, 2013
Published electronically: October 17, 2014
Communicated by: Daniel Ruberman
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.