Geodesic
The family Floer functor is faithful
Journal of the European Mathematical Society, Tome 19 (2017) no. 7, pp. 2139-2217

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Family Floer theory is used to construct a functor from the Fukaya category of a symplectic manifold admitting a Lagrangian torus fibration to a (twisted) category of perfect complexes on the mirror rigid analytic space. This functor is shown to be faithful by a degeneration argument involving moduli spaces of annuli.
DOI : 10.4171/jems/715
Classification : 53-XX, 14-XX
Keywords: Floer homology, Lagrangian torus fibration, rigid analytic spaces, coherent sheaves, homological mirror symmetry 
Mohammed Abouzaid. The family Floer functor is faithful. Journal of the European Mathematical Society, Tome 19 (2017) no. 7, pp. 2139-2217. doi: 10.4171/jems/715
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     author = {Mohammed Abouzaid},
     title = {The family {Floer} functor is faithful},
     journal = {Journal of the European Mathematical Society},
     pages = {2139--2217},
     year = {2017},
     volume = {19},
     number = {7},
     doi = {10.4171/jems/715},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/715/}
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