Starting with basic definitions of knots and knot types, the text proceeds to examinations of fundamental and free groups. A survey of the historic foundation for the notion of group presentation is followed by a careful proof of the theorem of Tietze and several examples of its use. Subsequent chapters explore the calculation of fundamental groups, the presentation of a knot group, the free calculus and the elementary ideals, and the knot polynomials and their characteristic properties. The text concludes with three helpful appendixes and a guide to the literature.
Starting with basic definitions of knots and knot types, the text proceeds to examinations of fundamental and free groups. A survey of the historic foundation for the notion of group presentation is followed by a careful proof of the theorem of Tietze and several examples of its use. Subsequent chapters explore the calculation of fundamental groups, the presentation of a knot group, the free calculus and the elementary ideals, and the knot polynomials and their characteristic properties. The text concludes with three helpful appendixes and a guide to the literature.
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