On Knots
eBook - PDF

On Knots

  1. 498 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

On Knots

About this book

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.

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Yes, you can access On Knots by Louis H. Kauffman in PDF and/or ePUB format, as well as other popular books in Mathematics & Topology. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover
  2. Title
  3. Copyright
  4. Dedication
  5. CONTENTS
  6. PREFACE
  7. I. INTRODUCTION
  8. II. LINKING NUMBERS AND REIDEMEISTER MOVES
  9. III. THE CONWAY POLYNOMIAL
  10. IV. EXAMPLES AND SKEIN THEORY
  11. V. DETECTING SLICES AND RIBBONS, A FIRST PASS
  12. VI. MISCELLANY
  13. VII. SPANNING SURFACES AND SEIFERT PAIRING
  14. VIII. RIBBONS AND SLICES
  15. IX. ALEXANDER POLYNOMIAL AND BRANCHED COVERINGS
  16. X. ALEXANDER POLYNOMIAL AND ARF INVARIANT
  17. XI. FREE DIFFERENTIAL CALCULUS
  18. XII. CYCLIC BRANCHED COVERINGS
  19. XIII. SIGNATURE THEOREMS
  20. XIV. G-SIGNATURE THEOREM FOR FOUR-MANIFOLDS
  21. XV. SIGNATURE OF CYCLIC BRANCHED COVERINGS
  22. XVI. AN INVARIANT FOR COVERINGS
  23. XVII. SLICE KNOTS
  24. XVIII. CALCULATING σr FOR GENERALIZED STEVEDORE'S KNOTS
  25. XIX. SINGULARITIES KNOTS AND BRIESKORN VARIETIES
  26. APPENDIX: Generalized Polynomials and a States Model for the Jones Polynomial
  27. TABLES: Knot Tables and the L-Polynomial
  28. REFERENCES