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.