Fukaya A_\infty-structures associated to Lefschetz fibrations. V

TL;DR

This paper explores the relationship between the Fukaya category of a Lefschetz fibration and its fiber, providing a more direct method to identify the associated bimodule homomorphism.

Contribution

It introduces a new, more direct approach to relate the Fukaya category of a Lefschetz fibration to that of its fiber, focusing on bimodule homomorphisms.

Findings

Established a direct identification of bimodule homomorphisms

Clarified the relationship between Fukaya categories of fibrations and fibers

Enhanced understanding of Fukaya category structures in Lefschetz fibrations

Abstract

We (re)consider how the Fukaya category of a Lefschetz fibration is related to that of the fibre. The distinguishing feature of the approach here is a more direct identification of the bimodule homomorphism involved.