5 citations · 10 across the 4 of their papers we have counts for
5 papers
Morse Homology, Tropical Geometry, and Homological Mirror Symmetry for Toric Varieties
Mohammed Abouzaid
Given a smooth projective toric variety X, we construct an A-infinity category of Lagrangians with boundary on a level set of the Landau-Ginzburg mirror of X. We prove that this ca…
On the Fukaya Categories of Higher Genus Surfaces
Mohammed Abouzaid
We construct the Fukaya category of a closed surface equipped with an area form using only elementary (essentially combinatorial) methods. We also compute the Grothendieck group of…
Homogeneous coordinate rings and mirror symmetry for toric varieties
Mohammed Abouzaid
Given a smooth toric variety X and an ample line bundle O(1), we construct a sequence of Lagrangian submanifolds of (C^*)^n with boundary on a level set of the Landau-Ginzburg mirr…
The moduli space of flat G-bundles on a compact hyper-Kahler manifold
Mohammed Abouzaid, Mitya Boyarchenko
We prove that if G is a compact connected Lie group and X is a compact connected hyper-Kahler manifold, then the L^2 metric on (the smooth locus of) the moduli space of flat G-bund…
Local structure of generalized complex manifolds
Mohammed Abouzaid, Mitya Boyarchenko
We study generalized complex manifolds from the point of view of symplectic and Poisson geometry. We start by showing that every generalized complex manifold admits a canonical Poi…