Abstract analogues of flux as symplectic invariants

TL;DR

This paper introduces new symplectic invariants derived from families of objects in Fukaya categories, focusing on their deformation behavior influenced by odd degree cohomology classes, with applications to blowups along symplectic mapping tori.

Contribution

It develops a novel approach to symplectic invariants using Fukaya categories and their deformation properties related to odd cohomology classes.

Findings

Defined new invariants of symplectic manifolds

Applied invariants to blowups along symplectic mapping tori

Enhanced understanding of deformation behavior in Fukaya categories

Abstract

We study families of objects in Fukaya categories, specifically ones whose deformation behaviour is prescribed by the choice of an odd degree cohomology class. This leads to invariants of symplectic manifolds, which we apply to blowups along symplectic mapping tori.