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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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Constructible sheaves and the Fukaya category
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by David Nadler and Eric Zaslow PDF
J. Amer. Math. Soc. 22 (2009), 233-286 Request permission

Abstract:

Let $X$ be a compact real analytic manifold, and let $T^*X$ be its cotangent bundle. Let $Sh(X)$ be the triangulated dg category of bounded, constructible complexes of sheaves on $X$. In this paper, we develop a Fukaya $A_\infty$-category $Fuk(T^*X)$ whose objects are exact, not necessarily compact Lagrangian branes in the cotangent bundle. We write $Tw Fuk(T^*X)$ for the $A_\infty$-triangulated envelope of $Fuk(T^*X)$ consisting of twisted complexes of Lagrangian branes. Our main result is that $Sh(X)$ quasi-embeds into $Tw Fuk(T^*X)$ as an $A_\infty$-category. Taking cohomology gives an embedding of the corresponding derived categories.
References
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Additional Information
  • David Nadler
  • Affiliation: Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, Illinois 60208
  • MR Author ID: 620327
  • Email: nadler@math.northwestern.edu
  • Eric Zaslow
  • Affiliation: Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, Illinois 60208
  • Email: zaslow@math.northwestern.edu
  • Received by editor(s): October 5, 2006
  • Published electronically: September 3, 2008
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 22 (2009), 233-286
  • MSC (2000): Primary 53D40, 32S60
  • DOI: https://doi.org/10.1090/S0894-0347-08-00612-7
  • MathSciNet review: 2449059