Abstract:A filling Dehn surface in a 3-manifold M is a generically immersed surface in M that induces a cellular decomposition of M. Given a tame link L in M there is a filling Dehn sphere of M that "trivializes" (diametrically splits) it. This allows to construct filling Dehn surfaces in the coverings of M branched over L. It is shown that one of the simplest filling Dehn spheres of S 3 (Banchoff's sphere) diametrically splits the trefoil knot. Filling Dehn spheres, and their Johansson diagrams, are constructed for th… Show more
Set email alert for when this publication receives citations?
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.