# Covariantly functorial wrapped Floer theory on Liouville sectors

## TL;DR

This paper introduces Liouville sectors and develops covariantly functorial wrapped Floer theory, enabling local-to-global analysis of symplectic invariants and advancing the understanding of Liouville manifolds with boundary.

## Contribution

It defines Liouville sectors and establishes covariant functoriality of wrapped Floer invariants, providing a new framework for local-to-global symplectic analysis.

## Key findings

- Definition of Liouville sectors
- Covariant functoriality of wrapped Fukaya category and symplectic cohomology
- A local-to-global principle for Abouzaid's generation criterion

## Abstract

We introduce a class of Liouville manifolds with boundary which we call Liouville sectors. We define the wrapped Fukaya category, symplectic cohomology, and the open-closed map for Liouville sectors, and we show that these invariants are covariantly functorial with respect to inclusions of Liouville sectors. From this foundational setup, a local-to-global principle for Abouzaid's generation criterion follows.