A topological model for the fukaya categories of plumbings

Mohammed Abouzaid MIT Department of Mathematics

Differential Geometry mathscidoc:1609.10205

Journal of Differential Geometry, 87, (1), 1-80, 2011
We prove that the algebra of singular cochains on a smooth manifold, equipped with the cup product, is equivalent to the A1 structure on the Lagrangian Floer cochain group associated to the zero section in the cotangent bundle. More generally, given embeddings with isomorphic normal bundles of a closed manifold B into manifolds Q1 and Q2, we construct a differential graded category from the singular cochains of these spaces, and prove that it is equivalent to the A1 category obtained by considering exact Lagrangian embeddings of Q1 and Q2 which intersect cleanly along B.
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@inproceedings{mohammed2011a,
  title={A TOPOLOGICAL MODEL FOR THE FUKAYA CATEGORIES OF PLUMBINGS},
  author={Mohammed Abouzaid},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911230507919607862},
  booktitle={Journal of Differential Geometry},
  volume={87},
  number={1},
  pages={1-80},
  year={2011},
}
Mohammed Abouzaid. A TOPOLOGICAL MODEL FOR THE FUKAYA CATEGORIES OF PLUMBINGS. 2011. Vol. 87. In Journal of Differential Geometry. pp.1-80. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911230507919607862.
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