Louis H. Kauffman Books

Focusing on knot theory as a means to explore mathematical physics, this book introduces knot and link invariants within a quantum-statistical framework. It emphasizes a combinatorial approach, facilitating access to algebra, combinatorial topology, and physical concepts. The content is divided into two parts: the first offers a foundational course on knots and physics, while the second presents lectures on related topics like frictional properties and dynamical systems. The new edition also includes discussions on Khovanov Homology and other relevant subjects.

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.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 The American Mathematical Monthly , March 1988.