Quilted Floer Cohomology

Abstract

We generalize Lagrangian Floer cohomology to sequences of Lagrangian correspondences. For sequences related by the geometric composition of Lagrangian correspondences we establish an isomorphism of the Floer cohomologies. We give applications to calculations of Floer cohomology, displaceability of Lagrangian correspondences, and transfer of displaceability under geometric composition.

minor corrections and updated references

References in corpus (4)

• Orientations for pseudoholomorphic quilts
• A symplectic Gysin sequence
• Floer Cohomology and Geometric Composition of Lagrangian Correspondences
• Lagrangian Floer homology of the Clifford torus and real projective space in odd dimensions

Cited by in corpus (37)

• The monotone wrapped Fukaya category and the open-closed string map
• Fukaya categories of symmetric products and bordered Heegaard-Floer homology
• Orientations for pseudoholomorphic quilts
• Fukaya categories of the torus and Dehn surgery
• The symplectic arc algebra is formal
• Fukaya Categories as Categorical Morse Homology
• Simplifying indefinite fibrations on 4-manifolds
• Dehn twists exact sequences through Lagrangian cobordism
• A-infinity functors for Lagrangian correspondences
• Gluing pseudoholomorphic quilted disks
• A new definition of Kuranishi space
• Floer field theory for tangles
• Quilted strips, graph associahedra, and A-infinity n-modules
• Wrapped Floer cohomology and Lagrangian correspondences
• Compactness results for neck-stretching limits of instantons
• Commuting symplectomorphisms and Dehn twists in divisors
• Bordered Floer homology and the spectral sequence of a branched double cover II: the spectral sequences agree
• Floer Cohomology and Geometric Composition of Lagrangian Correspondences
• Quilted Floer trajectories with constant components
• Topological defects as lagrangian correspondences
• A spectral sequence of the Floer cohomology of symplectomorphisms of trivial polarization class
• A monotone Lagrangian casebook
• Projective twists and the Hopf correspondence
• Higher-rank instanton cohomology and the quilted Atiyah-Floer conjecture
• A spectral sequence for Lagrangian Floer homology
• Floer cohomology and pencils of quadrics
• An index relation for the quilted Atiyah-Floer conjecture
• Tangles, relative character varieties, and holonomy perturbed traceless flat moduli spaces
• Iterations of symplectomorphisms and p-adic analytic actions on the Fukaya category
• Twin Lagrangian fibrations in mirror symmetry
• The equivariant pair-of-pants product in fixed point Floer cohomology
• Peterson conjecture via Lagrangian correspondences and wonderful compactifications
• Explicit constructions of quilts with seam condition coming from symplectic reduction
• A symplectic prolegomenon
• Algebraic sheaves of Floer homology groups via algebraic torus actions on the Fukaya category
• Algebraic Lagrangian cobordisms, flux and the Lagrangian Ceresa cycle
• Singularities of Lagrangian Immersions and its Applications in Lagrangian Floer Theory