Pseudoholomorphic Quilts

TL;DR

This paper introduces a new Floer theoretic framework using quilted pseudoholomorphic surfaces, leading to the construction of quantum homology morphisms linked to Lagrangian correspondences.

Contribution

It defines relative Floer invariants via quilted pseudoholomorphic surfaces and constructs quantum homology morphisms for monotone Lagrangian correspondences, advancing symplectic topology methods.

Findings

Defined relative Floer invariants from quilted pseudoholomorphic surfaces

Constructed a quantum homology morphism for monotone Lagrangian correspondences

Established new tools for symplectic topology and Floer theory

Abstract

We define relative Floer theoretic invariants arising from 'quilted pseudo-holomorphic surfaces': Collections of pseudoholomorphic maps to various target spaces with 'seam conditions' in Lagrangian correspondences. As application we construct a morphism on quantum homology associated to any monotone Lagrangian correspondence.