Squared Dehn twists and deformed symplectic invariants

TL;DR

This paper investigates the fragility of squared Dehn twists around even-dimensional Lagrangian spheres and computes their effects on symplectic cohomology in deformed settings, advancing understanding of symplectic invariants.

Contribution

It introduces an infinitesimal fragility concept for squared Dehn twists and computes twisted symplectic cohomology for specific Weinstein manifolds.

Findings

Fragility of squared Dehn twists established

Computed twisted symplectic cohomology for subflexible Weinstein manifolds

Demonstrated effects of deformations on symplectic invariants

Abstract

We establish an infinitesimal version of fragility for squared Dehn twists around even dimensional Lagrangian spheres. The precise formulation involves twisting the Fukaya category by a closed two-form or bulk deforming it by a half-dimensional cycle. As our main application, we compute the twisted and bulk deformed symplectic cohomology of the subflexible Weinstein manifolds constructed in \cite{murphysiegel}.