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Lagrangian cobordism and Fukaya categories

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Abstract

Given a symplectic manifold M we consider a category with objects finite ordered families of Lagrangian submanifolds of M (subject to certain additional constraints) and with morphisms Lagrangian cobordisms relating them. We construct a functor that maps this category to a variant of the derived Fukaya category of M in a way that takes into account the triangulated structure of the latter.

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Authors and Affiliations

  1. Department of Mathematics, ETH-Zürich, Rämistrasse 101, 8092, Zurich, Switzerland

    Paul Biran

  2. Department of Mathematics and Statistics, University of Montreal, C.P. 6128, Succ. Centre-Ville, Montreal, QC, H3C 3J7, Canada

    Octav Cornea

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  1. Paul Biran
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  2. Octav Cornea
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Correspondence to Paul Biran.

Additional information

Octav Cornea was supported by an NSERC Discovery grant and a FQRNT Group Research grant.

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Biran, P., Cornea, O. Lagrangian cobordism and Fukaya categories. Geom. Funct. Anal. 24, 1731–1830 (2014). https://doi.org/10.1007/s00039-014-0305-4

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