Formal Knot Theory

This exploration of combinatorics and knot theory is geared toward advanced undergraduates and graduate students. The author Louis H. Kauffman is a professor in the Department of Mathematics Statistics and Computer Science at the University of Illinois at Chicago. Kauffman draws upon his work as a topologist to illustrate the relationships between knot theory and statistical mechanics quantum theory and algebra as well as the role of knot theory in combinatorics.<br>Featured topics include state trails and the clock theorem; state polynomials and the duality conjecture; knots and links; axiomatic link calculations; spanning surfaces; the genus of alternative links; and ribbon knots and the Arf invariant. Key concepts are related in easy-to-remember terms and numerous helpful diagrams appear throughout the text. The author has provided a new supplement entitled Remarks on Formal Knot Theory as well as his article New Invariants in the Theory of Knots first published in <i>The American Mathematical Monthly</i> March 1988.