Graduate Texts in Mathematics

An Introduction to Knot Theory

Authors: Lickorish, W.B.Raymond

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About this Textbook

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.

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


Table of contents (16 chapters)

  • A Beginning for Knot Theory

    Lickorish, W. B. Raymond

    Pages 1-14

  • Seifert Surfaces and Knot Factorisation

    Lickorish, W. B. Raymond

    Pages 15-22

  • The Jones Polynomial

    Lickorish, W. B. Raymond

    Pages 23-31

  • Geometry of Alternating Links

    Lickorish, W. B. Raymond

    Pages 32-40

  • The Jones Polynomial of an Alternating Link

    Lickorish, W. B. Raymond

    Pages 41-48

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-1-4612-0691-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.95
price for USA
  • ISBN 978-0-387-98254-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $79.95
price for USA
  • ISBN 978-1-4612-6869-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
An Introduction to Knot Theory
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
175
Copyright
1997
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4612-0691-0
DOI
10.1007/978-1-4612-0691-0
Hardcover ISBN
978-0-387-98254-0
Softcover ISBN
978-1-4612-6869-7
Series ISSN
0072-5285
Edition Number
1
Number of Pages
X, 204
Topics