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  • Textbook
  • © 1997

An Introduction to Knot Theory

  • Written by an internationally acknowledged expert in the field who has won prizes for both exposition and research * Gives a comprehensive introduction to the field, presenting modern developments in the context of classical material * Will appeal to graduate students, mathematicians and physicists with a mathematical background who wish to gain new insights in this area

Part of the book series: Graduate Texts in Mathematics (GTM, volume 175)

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eBook USD 59.99
Price excludes VAT (USA)
  • ISBN: 978-1-4612-0691-0
  • Instant PDF download
  • Readable on all devices
  • Own it forever
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  • Tax calculation will be finalised during checkout
Softcover Book USD 79.95
Price excludes VAT (USA)
Hardcover Book USD 79.95
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Table of contents (16 chapters)

  1. Front Matter

    Pages i-x
  2. A Beginning for Knot Theory

    • W. B. Raymond Lickorish
    Pages 1-14
  3. Seifert Surfaces and Knot Factorisation

    • W. B. Raymond Lickorish
    Pages 15-22
  4. The Jones Polynomial

    • W. B. Raymond Lickorish
    Pages 23-31
  5. Geometry of Alternating Links

    • W. B. Raymond Lickorish
    Pages 32-40
  6. The Jones Polynomial of an Alternating Link

    • W. B. Raymond Lickorish
    Pages 41-48
  7. The Alexander Polynomial

    • W. B. Raymond Lickorish
    Pages 49-65
  8. Covering Spaces

    • W. B. Raymond Lickorish
    Pages 66-78
  9. The Conway Polynomial, Signatures and Slice Knots

    • W. B. Raymond Lickorish
    Pages 79-92
  10. Cyclic Branched Covers and the Goeritz Matrix

    • W. B. Raymond Lickorish
    Pages 93-102
  11. The Arf Invariant and the Jones Polynomial

    • W. B. Raymond Lickorish
    Pages 103-109
  12. The Fundamental Group

    • W. B. Raymond Lickorish
    Pages 110-122
  13. Obtaining 3-Manifolds by Surgery on S 3

    • W. B. Raymond Lickorish
    Pages 123-132
  14. 3-Manifold Invariants from the Jones Polynomial

    • W. B. Raymond Lickorish
    Pages 133-145
  15. Methods for Calculating Quantum Invariants

    • W. B. Raymond Lickorish
    Pages 146-165
  16. Generalisations of the Jones Polynomial

    • W. B. Raymond Lickorish
    Pages 166-178
  17. Exploring the HOMFLY and Kauffman Polynomials

    • W. B. Raymond Lickorish
    Pages 179-192
  18. Back Matter

    Pages 193-204

About this book

This account is an introduction to mathematical knot theory, the theory of knots and links of simple closed curves in three-dimensional space. Knots can be studied at many levels and from many points of view. They can be admired as artifacts of the decorative arts and crafts, or viewed as accessible intimations of a geometrical sophistication that may never be attained. The study of knots can be given some motivation in terms of applications in molecular biology or by reference to paral­ lels in equilibrium statistical mechanics or quantum field theory. Here, however, knot theory is considered as part of geometric topology. Motivation for such a topological study of knots is meant to come from a curiosity to know how the ge­ ometry of three-dimensional space can be explored by knotting phenomena using precise mathematics. The aim will be to find invariants that distinguish knots, to investigate geometric properties of knots and to see something of the way they interact with more adventurous three-dimensional topology. The book is based on an expanded version of notes for a course for recent graduates in mathematics given at the University of Cambridge; it is intended for others with a similar level of mathematical understanding. In particular, a knowledge of the very basic ideas of the fundamental group and of a simple homology theory is assumed; it is, after all, more important to know about those topics than about the intricacies of knot theory.

Keywords

  • Knot theory
  • Signatur
  • manifold
  • quantum invariant
  • topology

Reviews

W.B.R. Lickorish

An Introduction to Knot Theory

"This essential introduction to vital areas of mathematics with connections to physics, while intended for graduate students, should fall within the ken of motivated upper-division undergraduates."—CHOICE

Authors and Affiliations

  • Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, and Fellow of Pembroke College,Cambridge, Cambridge, England

    W. B. Raymond Lickorish

Bibliographic Information

Buying options

eBook USD 59.99
Price excludes VAT (USA)
  • ISBN: 978-1-4612-0691-0
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 79.95
Price excludes VAT (USA)
Hardcover Book USD 79.95
Price excludes VAT (USA)