Some Fibred Knots with Bi-orderable Knot Groups

This project aims to give an overview of knots, orderability of knot groups, and to construct knots for which the knot groups enjoy some nice properties. To accomplish this, we first present some preliminary results concerning knots and knot groups. We then introduce the Alexander polynomial, and explain the idea of a special polynomial originally introduced by Linnell, Rhemtulla and Rolfsen. By investigating the conditions on a special polynomial, we classify all the special Alexander polynomial of fibred knots of degree less than 10. Finally we construct examples of fibred knots which have a special Alexander polynomial.