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.
"Hopf bands in arborescent Hopf plumbings." Osaka J. Math. 56 (2) 375 - 389, April 2019.