On the existence of Hamiltonian 4-manifolds with a contact type boundary

TL;DR

This paper explores methods to construct Hamiltonian circle actions on 4-dimensional symplectic manifolds with contact type boundary, expanding the understanding of Hamiltonian group actions in this setting.

Contribution

It introduces new techniques for constructing Hamiltonian circle manifolds in dimension 4 with contact type boundary, advancing the study of such symplectic manifolds.

Findings

Several methods for constructing Hamiltonian circle manifolds in dimension 4

New insights into Hamiltonian group actions on manifolds with contact boundary

Extension of existing theories to manifolds with boundary

Abstract

While the Hamiltonian group actions on closed symplectic manifolds have been widely explored throughout the last couple of decades, the study on Hamiltonian group actions on symplectic manifolds with a contact type boundary has started only recently, with the work by Niederkr\"uger and the author [MN]. In this note we pursue this study by presenting several methods to construct such Hamiltonian circle manifolds in dimension 4.