Hopf bands in arborescent Hopf plumbings

TL;DR

This paper investigates the classification of Hopf bands in arborescent Hopf plumbings, revealing a connection to finite Coxeter groups and analyzing their homological and monodromic properties.

Contribution

It provides a classification of Seifert surfaces with finitely many Hopf bands, linking topological structures to algebraic Coxeter group classifications.

Findings

Finite classification of Hopf bands in certain Seifert surfaces

Connection between surface topology and Coxeter group theory

Insights into monodromy actions on Hopf bands

Abstract

For a positive Hopf plumbed arborescent Seifert surface $S$, we study the set of Hopf bands $H\subset S$, up to homology and up to the action of the monodromy. The classification of Seifert surfaces for which this set is finite is closely related to the classification of finite Coxeter groups.