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Springer Monographs in Mathematics

Surface-Knots in 4-Space

An Introduction

Authors: Kamada, Seiichi

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  • Is the first undergraduate textbook on surface knots, quandles, and two-dimensional braids
  • Includes a quick course on classical knot theory
  • Contains techniques for the motion picture method and quandle theory that are not only useful but essential for research
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eBook $89.00
price for USA in USD (gross)
  • ISBN 978-981-10-4091-7
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $119.00
price for USA in USD
  • ISBN 978-981-10-4090-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $119.00
price for USA in USD
  • ISBN 978-981-13-5046-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

This introductory volume provides the basics of surface-knots and related topics, not only for researchers in these areas but also for graduate students and researchers who are not familiar with the field.Knot theory is one of the most active research fields in modern mathematics. Knots and links are closed curves (one-dimensional manifolds) in Euclidean 3-space, and they are related to braids and 3-manifolds. These notions are generalized into higher dimensions. Surface-knots or surface-links are closed surfaces (two-dimensional manifolds) in Euclidean 4-space, which are related to two-dimensional braids and 4-manifolds. Surface-knot theory treats not only closed surfaces but also surfaces with boundaries in 4-manifolds. For example, knot concordance and knot cobordism, which are also important objects in knot theory, are surfaces in the product space of the 3-sphere and the interval.Included in this book are basics of surface-knots and the related topics of classical knots, the motion picture method, surface diagrams, handle surgeries, ribbon surface-knots, spinning construction, knot concordance and 4-genus, quandles and their homology theory, and two-dimensional braids.

Reviews

“Kamada provides a discussion of a great deal of important machinery and current approaches to both knot theory in the more familiar and prosaic sense as well as the more exotic surface-knot theory, the book’s main focus. … is well-written, theorems are plentiful and proven, there are a huge number of diagrams and pictures … there are lots of examples, and there are even exercises. This book indeed looks like a good place to learn about surface knots in 4-space.” (Michael Berg, MAA Reviews, December, 2017)


Table of contents (10 chapters)

Table of contents (10 chapters)

Buy this book

eBook $89.00
price for USA in USD (gross)
  • ISBN 978-981-10-4091-7
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $119.00
price for USA in USD
  • ISBN 978-981-10-4090-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $119.00
price for USA in USD
  • ISBN 978-981-13-5046-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Surface-Knots in 4-Space
Book Subtitle
An Introduction
Authors
Series Title
Springer Monographs in Mathematics
Copyright
2017
Publisher
Springer Singapore
Copyright Holder
Springer Nature Singapore Pte Ltd.
eBook ISBN
978-981-10-4091-7
DOI
10.1007/978-981-10-4091-7
Hardcover ISBN
978-981-10-4090-0
Softcover ISBN
978-981-13-5046-7
Series ISSN
1439-7382
Edition Number
1
Number of Pages
XI, 212
Number of Illustrations
146 b/w illustrations
Topics