Bouquets of curves in surfaces

TL;DR

This paper characterizes when a set of simple closed curves on an orientable surface forms a bouquet by analyzing the relations between their corresponding Dehn twists.

Contribution

It provides a new characterization of bouquets of curves in surfaces using relations among Dehn twists, advancing understanding in surface topology.

Findings

Identifies conditions under which curves form a bouquet

Relates curve configurations to Dehn twist relations

Enhances understanding of surface curve arrangements

Abstract

We characterise when a set of simple closed curves in an orientable surface forms a bouquet, in terms of relations between the corresponding Dehn twists.