Article
Kyungpook Mathematical Journal 2020; 60(4): 831-837
Published online December 31, 2020
Copyright © Kyungpook Mathematical Journal.
Klein Bottles and Dehn Filling on a Component of Twocomponent Link Exterior
Nabil Sayari
Département de Mathématiques et de Statistique, Université de Moncton, Moncton, Nouveau-Brunswick, Canada
e-mail : nabil.sayari@umoncton.ca
Received: November 20, 2019; Revised: July 17, 2020; Accepted: July 21, 2020
Let M be the exterior of a hyperbolic link K ∪ L in a homology 3-sphere Y, such that the linking number lk(K, L) is non-zero. In this note we prove that if γ is a slope in ∥N(L) such that the manifold ML(γ) obtained by γ-Dehn filling along ∥ N(L) contains a Klein bottle, then there is a bound on Δ (µ, γ), depending on the genus of K and on lk(K, L).
Keywords: Dehn filling, essential surface, Klein bottle, Scharlemann cycle