Moduli spaces of semitoric systems

TL;DR

This paper explores the classification of semitoric integrable systems using symplectic invariants, introduces a family of metrics on their space, and constructs the metric space's completion.

Contribution

It defines a new family of metrics on semitoric systems and constructs their completion, advancing the understanding of their geometric structure.

Findings

The metric space of semitoric systems is incomplete.

A natural completion of this metric space is constructed.

The classification by symplectic invariants facilitates this metric structure.

Abstract

Recently Pelayo-V\~{u} Ngoc classified semitoric integrable systems in terms of five symplectic invariants. Using this classification we define a family of metrics on the space of semitoric integrable systems. The resulting metric space is incomplete and we construct the completion.