Non-triviality of welded knots and ribbon torus-knots

Abstract

In this paper we study welded knots and their invariants. We focus on generating examples of non-trivial knotted ribbon tori as the tube of welded knots that are obtained from classical knot diagrams by welding some of the crossings. Non-triviality is shown by determining the fundamental group of the concerned welded knot. Sample examples under consideration are the standard diagrams of the family of $(2,q)$ torus knots and the twist knots. Standard diagrams of knots from Rolfsen's tables with $6$ crossings are also discussed which are not in the family of torus and twist knots.