On the Fukaya categories of higher genus surfaces

  title={On the Fukaya categories of higher genus surfaces},
  author={Mohammed Abouzaid},
  journal={Advances in Mathematics},
  • M. Abouzaid
  • Published 23 June 2006
  • Mathematics
  • Advances in Mathematics
A Geometric Proof of a Faithful Linear-Categorical Surface Mapping Class Group Action
We give completely combinatorial proofs of the main results of [3] using polygons. Namely, we prove that the mapping class group of a surface with boundary acts faithfully on a finitely-generated
Lagrangian cobordism groups of higher genus surfaces
We study Lagrangian cobordism groups of oriented surfaces of genus greater than two. We compute the immersed oriented Lagrangian cobordism group of these surfaces. We show that a variant of this
We study the derived Hall algebra of the partially wrapped Fukaya category of a surface. We give an explicit description of the Hall algebra for the disk with $m$ marked intervals and we give a
The Lagrangian cobordism group of $$T^2$$T2
We compute the Lagrangian cobordism group of the standard symplectic 2-torus and show that it is isomorphic to the Grothendieck group of its derived Fukaya category. The proofs use homological mirror
The Fukaya Category of the Elliptic Curve as an Algebra over the Feynman Transform
UNIVERSITY OF CALIFORNIA, SAN DIEGO The Fukaya Category of the Elliptic Curve as an Algebra over the Feynman Transform A dissertation submitted in partial satisfaction of the requirements for the
Groupes de cobordisme lagrangien immergé et structure des polygones pseudo-holomorphes
We explain how to generalize Lazzarini’s structural Theorem from [Laz11] to the case of curves with boundary on a given Lagrangian immersion. As a consequence of this result, we show that we can
Homological Mirror Symmetry and Algebraic Cycles
In this chapter we outline some applications of Homological Mirror Symmetry to classical problems in Algebraic Geometry, like rationality of algebraic varieties and the study of algebraic cycles.
We derive a formula expanding the bracket with respect to a natural deformation parameter. The expansion is in terms of a two-variable polynomial algebra of diagram resolutions generated by basic


Vanishing Cycles and Mutation
Using Floer cohomology, we establish a connection between PicardLefschetz theory and the notion of mutation of exceptional collections in homological algebra.
Exact Lagrangian Submanifolds in T*S n and the Graded Kronecker Quiver
This short and fairly informal note is an attempt to explain how methods of homological algebra may be brought to bear on problems in symplectic geometry. We do this by looking at a familiar sample
Categorical Mirror Symmetry: The Elliptic Curve
We describe an isomorphism of categories conjectured by Kontsevich. If M and f M are mirror pairs then the conjectural equivalence is between the derived category of coherent sheaves on M and a
Massey and Fukaya products on elliptic curves
This note is a continuation of our paper with E. Zaslow "Categorical mirror symmetry: the elliptic curve", math.AG/9801119. We compare some triple Massey products on elliptic curve with the
Homological mirror symmetry for the quartic surface
This proves Kontsevich's mirror conjecture for (on the symplectic side) a quartic surface in P^3.
Exact Lagrangian submanifolds in simply-connected cotangent bundles
We consider exact Lagrangian submanifolds in cotangent bundles. Under certain additional restrictions (triviality of the fundamental group of the cotangent bundle, and of the Maslov class and second
Two theorems on the mapping class group of a surface
The mapping class group of a closed surface of genus > 3 is perfect. An infinite set of generators is given for the subgroup of maps that induce the identity on homology. Let Tg be the boundary of a
Moment maps, monodromy and mirror manifolds
Via considerations of symplectic reduction, monodromy, mirror symmetry and Chern-Simons functionals, a conjecture is proposed on the existence of special Lagrangians in the hamiltonian deformation
More about vanishing cycles and mutation
The paper continues the discussion of symplectic aspects of Picard-Lefschetz theory begun in "Vanishing cycles and mutation" (this archive). There we explained how to associate to a suitable