Synopses & Reviews
This exploration of combinatorics and knot theory is geared toward advanced undergraduates and graduate students and features new appendixes on recent developments. A professor in the Department of Mathematics, Statistics, and Computer Science at the University of Illinois at Chicago, Louis H. Kauffman is a topologist who works with knot theory and its relationships with statistical mechanics, quantum theory, and algebra, as well as with combinatorics.
Synopsis
This exploration of combinatorics and knot theory is geared toward advanced undergraduates and graduate students. The author 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. 1983 edition. Includes 51 illustrations.
Synopsis
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.
Table of Contents
1. Introduction
2. State, Trails, and the Clock Theorem
3. State Polynomials and the Duality Conjecture
4. Knots and Links
5. Axiomatic Link Calculations
6. Curliness and the Alexander Polynomial
7. The Coat of Many Colors
8. Spanning Surfaces
9. The Genus of Alternative Links
10. Ribbon Knots and the Arf Invariant
Appendix. The Classical Alexander Polynomial
References