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

TL;DR

This paper studies Hamiltonian Floer cohomology in Lefschetz fibrations, focusing on the algebraic structures and connections that differentiate with respect to the Novikov variable, advancing understanding of symplectic topology.

Contribution

It introduces a framework for equipping Floer cohomology groups with connections in the context of Lefschetz fibrations, under specific assumptions, enhancing the algebraic structure analysis.

Findings

Floer cohomology groups associated to Lefschetz fibrations are analyzed.

Connections differentiating with respect to the Novikov variable are constructed.

The approach relies on an important additional assumption.

Abstract

We consider Hamiltonian Floer cohomology groups associated to a Lefschetz fibration, and the structure of operations on them. As an application, we will (under an important additional assumption) equip those groups with connections, which differentiate with respect to the Novikov variable.