Calabi-Yau structures on Rabinowitz Fukaya categories

TL;DR

This paper proves that under certain conditions, the derived Rabinowitz Fukaya category of a Liouville domain exhibits a Calabi-Yau structure of dimension n-1, linking it to the wrapped Fukaya category.

Contribution

It establishes the Calabi-Yau property of the derived Rabinowitz Fukaya category assuming specific generation and finiteness conditions on the wrapped Fukaya category.

Findings

Derived Rabinowitz Fukaya category is (n-1)-Calabi-Yau under conditions.

Links between Rabinowitz and wrapped Fukaya categories are established.

Provides conditions for Calabi-Yau structures in symplectic topology.

Abstract

In this paper, we prove that the derived Rabinowitz Fukaya category of a Liouville domain $M$ of dimension $2n$ is $(n-1)$-Calabi--Yau assuming the wrapped Fukaya category of $M$ admits an at most countable set of Lagrangians that generate it and satisfy some finiteness condition on morphism spaces between them.