Orientations for pseudoholomorphic quilts

Abstract

We construct orientations on moduli spaces of pseudoholomorphic quilts with seam conditions in Lagrangian correspondences equipped with relative spin structures and determine the effect of various gluing operations on the orientations. We also investigate the behavior of the orientations under composition of Lagrangian correspondences.

74 pages, 13 figures. A few added paragraphs on disk potentials and a few typos fixed

References in corpus (5)

• Intersection theory on the moduli space of holomorphic curves with Lagrangian boundary conditions
• A-infinity functors for Lagrangian correspondences
• Gluing pseudoholomorphic quilted disks
• Source Spaces and Perturbations for Cluster Complexes
• Differential Geometry of Relative Gerbes

Cited by in corpus (18)

• The Lagrangian Floer-quantum-PSS package and canonical orientations in Floer theory
• Floer theory and flips
• Point-like bounding chains in open Gromov-Witten theory
• Floer homology of Lagrangians in clean intersection
• A-infinity functors for Lagrangian correspondences
• Functors of wrapped Fukaya categories from Lagrangian correspondences
• Floer field theory for tangles
• Differential forms, Fukaya $A_{\infty }$ algebras, and Gromov-Witten axioms
• Arnold Conjecture and Morava K-theory
• Fukaya algebras via stabilizing divisors
• Wrapped Floer cohomology and Lagrangian correspondences
• Orientations of Morse flow trees in Legendrian contact homology
• Hamiltonian no-torsion
• A monotone Lagrangian casebook
• The cyclic open-closed map, u-connections and R-matrices
• Applications of the theory of Floer to symmetric spaces
• Relative quantum cohomology of the Chiang Lagrangian
• Peterson conjecture via Lagrangian correspondences and wonderful compactifications