A01=Louis H. Kauffman
Addition theorem
Alexander polynomial
Algebraic variety
Algorithm
Ambient isotopy
Arf invariant
Author_Louis H. Kauffman
Bijection
Bilinear form
Borromean rings
Bracket polynomial
Braid group
Branched covering
Category=PBPD
Category=PBV
Chiral knot
Chromatic polynomial
Cobordism
Codimension
Combinatorics
Connected sum
Conway polynomial (finite fields)
Counting
Covering space
Cyclic group
Determinant
Diagram (category theory)
Diffeomorphism
Disjoint union
Disk (mathematics)
Dual graph
Embedding
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Fibration
Formal power series
Fundamental group
Geometry
Geometry and topology
Homotopy
Intersection form (4-manifold)
Jones polynomial
Knot complement
Knot group
Knot theory
Laws of Form
Linking number
Manifold
Module (mathematics)
Morwen Thistlethwaite
Notation
Obstruction theory
Operator algebra
Pairing
Planar graph
Point at infinity
Polynomial
Polynomial ring
Reidemeister move
Saddle point
Seifert surface
Singularity theory
Slice knot
Special case
Substructure
Summation
Theorem
Topological space
Torus knot
Trefoil knot
Unknot
Variable (mathematics)
Whitehead link
Wild knot
Writhe
Product details
- ISBN 9780691084350
- Weight: 680g
- Dimensions: 152 x 235mm
- Publication Date: 21 Oct 1987
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
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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.
