Non-triviality of welded knots and ribbon torus-knots

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 families of ( 2 , q ) (2,q) -torus knots and twist knots. The standard diagrams of knots from Rolfsen’s tables with 6 6 crossings are also discussed which are not in the family of torus and twist knots.