A note on the support norm of a contact structure

TL;DR

This paper shows that for contact structures, three invariants introduced by Etnyre and Ozbagci—support genus, binding number, and support norm—are mutually determining, linking their values closely.

Contribution

It establishes that the support genus, binding number, and support norm invariants for contact structures uniquely determine each other.

Findings

Support invariants are mutually determining for contact structures.

The invariants provide a complete characterization when considered together.

This insight simplifies the understanding of contact structure invariants.

Abstract

In this note we observe that the no two of the three invariants defined for contact structures by Etnyre and Ozbagci -- that is, the support genus, binding number and support norm -- determine the third.