On Knots. (Am-115), Volume 115 Contributor(s): Kauffman, Louis H. (Author) |
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ISBN: 0691084351 ISBN-13: 9780691084350 Publisher: Princeton University Press OUR PRICE: $133.95 Product Type: Paperback - Other Formats Published: October 1987 |
Additional Information |
BISAC Categories: - Mathematics | Topology - General - Mathematics | Geometry - General |
Dewey: 514.224 |
LCCN: 87003195 |
Series: Annals of Mathematics Studies (Paperback) |
Physical Information: 1.17" H x 6.16" W x 9.26" (1.51 lbs) 498 pages |
Descriptions, Reviews, Etc. |
Publisher Description: On Knots is a journey through the theory of knots, starting from the simplest combinatorial ideas--ideas arising from the representation of weaving patterns. From this beginning, topological invariants are constructed directly: first linking numbers, then the Conway polynomial and skein theory. This paves the way for later discussion of the recently discovered Jones and generalized polynomials. The central chapter, Chapter Six, is a miscellany of topics and recreations. Here the reader will find the quaternions and the belt trick, a devilish rope trick, Alhambra mosaics, Fibonacci trees, the topology of DNA, and the author's geometric interpretation of the generalized Jones Polynomial. Then come branched covering spaces, the Alexander polynomial, signature theorems, the work of Casson and Gordon on slice knots, and a chapter on knots and algebraic singularities.The book concludes with an appendix about generalized polynomials. |