Modern Birkhäuser Classics

Knot Theory and Its Applications

Authors: Murasugi, Kunio

  • Includes fundamental mathematical concepts as well as applications to physics, biology and chemistry
  • Motivates the reader with historical background and notes
  • Balances theory with visualization in over 300 illustrations
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eBook $34.99
price for USA (gross)
  • ISBN 978-0-8176-4719-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $44.95
price for USA
  • ISBN 978-0-8176-4718-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

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

Reviews

From the reviews:

"The book ...develops knot theory from an intuitive geometric-combinatorial point of view, avoiding completely more advanced concepts and techniques from algebraic topology.... intended for readers without a considerable background in mathematics...particular attention is given to connections and applications to other natural sciences. 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

"Noteworthy features here include applications to chemistry and biology and a final chapter on the very important Vassiliev invariants, a fairly late-breaking development. Murasugi, an expert of stature on knots, begins absolutely from first principles and avoids sophisticated terminology, but he writes in a careful and rigorous style."   –Choice

"I grabbed the opportunity to review this book, and I’m still enthusiastic. … I enjoyed it immensely. … In general, the author strives for clarity, and that was appreciated by this reviewer and will be appreciated by students. … I also enjoyed how he always keeps us abreast of the general picture, in particular keeping us up to date with respect to the various new results and successes … ." (Marion Cohen, MathDL, June, 2008)


Table of contents (16 chapters)

Buy this book

eBook $34.99
price for USA (gross)
  • ISBN 978-0-8176-4719-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $44.95
price for USA
  • ISBN 978-0-8176-4718-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Knot Theory and Its Applications
Authors
Series Title
Modern Birkhäuser Classics
Copyright
1996
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-0-8176-4719-3
DOI
10.1007/978-0-8176-4719-3
Softcover ISBN
978-0-8176-4718-6
Series ISSN
2197-1803
Edition Number
1
Number of Pages
X, 341
Topics