Affiliation:
1. School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, P. R. China
Abstract
In this paper, we give a necessary condition for detecting (possibly punctured) closed incompressible meridionally incompressible surfaces in knot or link complements. This condition provides us a method to determine whether an arbitrary link is split or non-split based on the link diagram. We also prove that, up to isotopy, there only exist finitely many such surfaces in non-split prime almost alternating link complements. Finally, we demonstrate an application of the necessary condition by showing elementary by-hand proofs that some certain knots are small knots.
Publisher
World Scientific Pub Co Pte Ltd
Subject
Algebra and Number Theory