Geometric composition in quilted Floer theory

TL;DR

This paper proves the invariance of Floer cohomology for cyclic Lagrangian correspondences under composition, with an added monotonicity assumption to prevent bubbling, advancing the understanding of Floer theory.

Contribution

It establishes invariance of Floer cohomology under composition of Lagrangians and introduces a monotonicity condition to handle bubbling issues.

Findings

Floer cohomology remains invariant under composition of Lagrangian correspondences.

A new monotonicity assumption is introduced to prevent bubbling at the Y-end.

The results extend the applicability of Floer theory to more complex Lagrangian configurations.

Abstract

We prove that Floer cohomology of cyclic Lagrangian correspondences is invariant under transverse and embedded composition of Lagrangians under a general set of assumptions. In the Corrigendum, we introduce an additional assumption of monotonicity for cylinders which is needed to avoid bubbling at the Y-end.