Knot Theory and Its Applications

  • Kunio Murasugi

Part of the Modern Birkhäuser Classics book series (MBC)

Table of contents

  1. Front Matter
    Pages i-x
  2. Kunio Murasugi
    Pages 1-4
  3. Kunio Murasugi
    Pages 5-24
  4. Kunio Murasugi
    Pages 25-39
  5. Kunio Murasugi
    Pages 40-46
  6. Kunio Murasugi
    Pages 47-74
  7. Kunio Murasugi
    Pages 75-103
  8. Kunio Murasugi
    Pages 104-131
  9. Kunio Murasugi
    Pages 132-151
  10. Kunio Murasugi
    Pages 152-170
  11. Kunio Murasugi
    Pages 171-196
  12. Kunio Murasugi
    Pages 197-216
  13. Kunio Murasugi
    Pages 217-247
  14. Kunio Murasugi
    Pages 248-266
  15. Kunio Murasugi
    Pages 267-283
  16. Kunio Murasugi
    Pages 284-298
  17. Kunio Murasugi
    Pages 298-323
  18. Back Matter
    Pages 225-341

About this book

Introduction

Knot theory is a concept in algebraic topology that has found applications to a variety of mathematical problems as well as to problems in computer science, biological and medical research, and mathematical physics. This book is directed to a broad audience of researchers, beginning graduate students, and senior undergraduate students in these fields.

The book contains most of the fundamental classical facts about the theory, such as knot diagrams, braid representations, Seifert surfaces, tangles, and Alexander polynomials; also included are key newer developments and special topics such as chord diagrams and covering spaces. The work introduces the fascinating study of knots and provides insight into applications to such studies as DNA research and graph theory. In addition, each chapter includes a supplement that consists of interesting historical as well as mathematical comments.

The author clearly outlines what is known and what is not known about knots. He has been careful to avoid advanced mathematical terminology or intricate techniques in algebraic topology or group theory. There are numerous diagrams and exercises relating the material. The study of Jones polynomials and the Vassiliev invariants are closely examined.

"The book ...develops knot theory from an intuitive geometric-combinatorial point of view, avoiding completely more advanced concepts and techniques from algebraic topology...Thus the emphasis is on a lucid and intuitive exposition accessible to a broader audience... The book, written in a stimulating and original style, will serve as a first approach to this interesting field for readers with various backgrounds in mathematics, physics, etc. It is the first text developing recent topics as the Jones polynomial and Vassiliev invariants on a level accessible also for non-specialists in the field." -Zentralblatt Math

Keywords

Algebraic topology Knot invariant Knot theory computer computer science group theory mathematical physics

Authors and affiliations

  • Kunio Murasugi
    • 1
  1. 1.Department of MathematicsUniversity of TorontoTorontoCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-8176-4719-3
  • Copyright Information Springer Science+Business Media New York 1996
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-8176-4718-6
  • Online ISBN 978-0-8176-4719-3
  • About this book