ENGLISH

On Knots.

By Louis H. Kauffman

Book information

Publisher
Princeton University Press
Year
1988
ISBN
9781400882137, 1400882133
Language
english
Format
PDF
Filesize
10 MB (10280003 bytes)
Series
Annals of Mathematics Studies 115
Pages
498\496
Time added
2021-10-31 11:54:14

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. 0.1 0.2 0.3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

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