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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

Lagrangian cobordism. I


Authors: Paul Biran and Octav Cornea
Journal: J. Amer. Math. Soc. 26 (2013), 295-340
MSC (2010): Primary 53D12, 53D40; Secondary 57D37
Published electronically: December 10, 2012
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Abstract: We discuss Lagrangian cobordism between Lagrangian submanifolds (in the monotone setting) and we show that Lagrangian Floer and quantum homologies are rigid with respect to this type of cobordism. We also discuss obstructions to cobordism based on properties of Lagrangian quantum homology, relations to Lagrangian surgery, as well as examples of non-isotopic but cobordant Lagrangians. Finally, Lagrangian cobordism is used to structure the respective class of Lagrangians as a category and the results of the paper are interpreted as indicating the existence of a functor defined on this category with values in an appropriate (derived) Fukaya category and which is compatible with the triangulated structure of the target.


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Additional Information

Paul Biran
Affiliation: Department of Mathematics, ETH-Zürich, Rämistrasse 101, 8092 Zürich, Switzerland
Email: biran@math.ethz.ch

Octav Cornea
Affiliation: Department of Mathematics and Statistics, University of Montreal, C.P. 6128 Succ. Centre-Ville Montreal, QC H3C 3J7, Canada
Email: cornea@dms.umontreal.ca

DOI: http://dx.doi.org/10.1090/S0894-0347-2012-00756-5
PII: S 0894-0347(2012)00756-5
Received by editor(s): October 11, 2011
Received by editor(s) in revised form: August 9, 2012
Published electronically: December 10, 2012
Additional Notes: The second author was supported by an NSERC Discovery grant and a FQRNT Group Research grant
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.