Surface-Knots in 4-Space

An Introduction

  • Seiichi┬áKamada

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Seiichi Kamada
    Pages 1-13
  3. Seiichi Kamada
    Pages 15-37
  4. Seiichi Kamada
    Pages 39-73
  5. Seiichi Kamada
    Pages 75-87
  6. Seiichi Kamada
    Pages 89-104
  7. Seiichi Kamada
    Pages 105-113
  8. Seiichi Kamada
    Pages 115-124
  9. Seiichi Kamada
    Pages 125-155
  10. Seiichi Kamada
    Pages 157-172
  11. Seiichi Kamada
    Pages 173-195
  12. Back Matter
    Pages 197-212

About this book

Introduction

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.

Keywords

Surface knot Quandle and quandle homology 2-dimensional braid Motion picture Surface diagram

Authors and affiliations

  • Seiichi┬áKamada
    • 1
  1. 1.Graduate School of ScienceOsaka City UniversityOsakaJapan

Bibliographic information

  • DOI https://doi.org/10.1007/978-981-10-4091-7
  • Copyright Information Springer Nature Singapore Pte Ltd. 2017
  • Publisher Name Springer, Singapore
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-981-10-4090-0
  • Online ISBN 978-981-10-4091-7
  • Series Print ISSN 1439-7382
  • Series Online ISSN 2196-9922
  • About this book