157 citations · 536 across the 39 of their papers we have counts for
4 papers · 2 filters
Altering symplectic manifolds by homologous recombination
Mohammed Abouzaid, Paul Seidel
We use symplectic cohomology to study the non-uniqueness of symplectic structures on the smooth manifolds underlying affine varieties. Starting with a Lefschetz fibration on such a…
Nearby Lagrangians with vanishing Maslov class are homotopy equivalent
Mohammed Abouzaid
We prove that the inclusion of every closed exact Lagrangian with vanishing Maslov class in a cotangent bundle is a homotopy equivalence. We start by adapting an idea of Fukaya-Sei…
A cotangent fibre generates the Fukaya category
Mohammed Abouzaid
We prove that the algebra of chains on the based loop space recovers the derived (wrapped) Fukaya category of the cotangent bundle of a closed smooth orientable manifold. The main…
A geometric criterion for generating the Fukaya category
Mohammed Abouzaid
Given a collection of exact Lagrangians in a Liouville manifold, we construct a map from the Hochschild homology of the Fukaya category that they generate to symplectic cohomology.…