2024/11/15 by Jae Choon Cha, Cha, Jae Choon, Min Hoon Kim +1
Mathematics · Decision Sciences · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Fuzzy and Soft Set Theory
paper · pdf · doi:10.48550/arxiv.2411.10051
In 2009, Calegari constructed smooth homotopy 4-spheres from monodromies of fibered knots. We prove that all these are diffeomorphic to the standard 4-sphere. Our method uses 5-dimensional handlebody techniques and results on mapping class groups of 3-dimensional handlebodies. As an application, we present potential counterexamples to the smooth 4-dimensional Schoenflies conjecture which are related to the work of Casson and Gordon on fibered ribbon knots.