Hopf Arborescent Links, Minor Theory, and Decidability of the Genus Defect

Learn about advanced knot theory concepts in this mathematics research lecture that explores the computational challenges of four-dimensional knot genus variants. Delve into the investigation of Hopf arborescent links, formed as boundaries of iterated Hopf band plumbings, and discover how their genus defects can be computed through decidable methods. Explore the non-constructive proof methodology that demonstrates how Seifert surfaces of these specialized links form a well-quasi-order under minor relations, providing new insights into the relationship between classical and four-dimensional genera in both smooth and topological locally flat categories.