Symplectic dynamics of contact isotropic torus complements

TL;DR

This paper investigates the topology of isotropic torus complements in contact manifolds by linking it to Reeb dynamics, using advanced holomorphic curve techniques from symplectic field theory.

Contribution

It provides a novel description of the homotopy type of isotropic torus complements based on Reeb dynamics and holomorphic curve methods.

Findings

Homotopy type characterized in terms of Reeb dynamics

Application of Gromov-Hofer compactness in contact topology

New insights into contact isotropic torus complements

Abstract

We determine the homotopy type of isotropic torus complements in closed contact manifolds in terms of Reeb dynamics of special contact forms. For that we utilize holomorphic curve techniques known from symplectic field theory as Gromov-Hofer compactness and localized transversality on non-compact contact manifolds.