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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Lagrangian cobordism. I
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by Paul Biran and Octav Cornea PDF
J. Amer. Math. Soc. 26 (2013), 295-340 Request permission

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.
References
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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
  • MR Author ID: 346358
  • Email: cornea@dms.umontreal.ca
  • 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
  • © Copyright 2012 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 26 (2013), 295-340
  • MSC (2010): Primary 53D12, 53D40; Secondary 57D37
  • DOI: https://doi.org/10.1090/S0894-0347-2012-00756-5
  • MathSciNet review: 3011416