The article explores the decidability of computing the genus defect in a class of knots and links known as Hopf arborescent links. It discusses the structure of these links obtained from plumbings of Hopf bands, showing that their 4-dimensional invariants can be determined. The study focuses on Seifert surfaces and minor theory to establish well-quasi-orders for these surfaces. The construction process involves plane trees and iterative plumbings, leading to fibred surfaces with minimal genus. The paper also delves into related work on arborescent knots and general plumbing structures, highlighting the unique properties of Hopf arborescent links.
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by Pierre Dehor... alle arxiv.org 03-19-2024
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