Constructible sheaves and the Fukaya category
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- by David Nadler and Eric Zaslow
- J. Amer. Math. Soc. 22 (2009), 233-286
- DOI: https://doi.org/10.1090/S0894-0347-08-00612-7
- Published electronically: September 3, 2008
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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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Bibliographic 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