# Rabinowitz Floer homology and mirror symmetry

## TL;DR

The paper introduces a new invariant for Liouville cobordisms using symplectic cohomology, computes it for specific bundles, and explores its implications through mirror symmetry and Lagrangian Floer homology.

## Contribution

It defines a novel invariant of Liouville cobordisms, computes it in key examples, and connects it to mirror symmetry and Floer homology results.

## Key findings

- Invariant is non-trivial for certain bundles
- Computed invariant for annulus subbundles of tautological bundles
- Proved non-vanishing result related to Lagrangian Floer homology

## Abstract

We define a quantitative invariant of Liouville cobordisms with monotone filling through an action-completed symplectic cohomology theory. We illustrate the non-trivial nature of this invariant by computing it for annulus subbundles of the tautological bundle over $\mathbb{C} P^1$ and give further conjectural computations based on mirror symmetry. We prove a non-vanishing result in the presence of Lagrangian submanifolds with non-vanishing Floer homology.