A partial order on multibranched surfaces in 3-manifolds

摘要

In this paper, we introduce a partial order on neighborhood equivalence classes of maximally spread essential multibranched surfaces embedded in a 3-manifold. We show that if a maximally spread essential multibranched surface is atoroidal and acylindrical, then its equivalence class is minimal with respect to the partial order. (C) 2020 Elsevier B.V. All rights reserved.