Additivity of support norm of tight contact structures

TL;DR

This paper proves that the support norm of tight contact structures is additive, meaning the support norm of a combined structure equals the sum of the individual norms, advancing understanding of contact topology.

Contribution

It establishes the additivity property of the support norm specifically for tight contact structures, a new result in contact topology.

Findings

Support norm is additive for tight contact structures.

Provides a new tool for analyzing contact structures.

Enhances understanding of the relationship between open books and contact structures.

Abstract

The support norm $sn(\xi)$ of a contact structure $\xi$ is the minimum of the negative Euler characteristics of the pages of the open books supporting $\xi$. In this paper we prove additivity of the support norm for tight contact structures.