Surface-knots in 4-space : an introduction

Bibliographic Information

Surface-knots in 4-space : an introduction

Seiichi Kamada

Springer Nature Singapore, c2017 , [Books on Demand]

  • : [hardcover]

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Note

[Reprint]. Originally published: Singapore : Springer Nature Singapore , c2017

"Printed by Books on demand, Germany"--P. [214]

Originally issued in the series: Springer monographs in mathematics

Includes bibliographical references (p. 199-205) and index

Description and Table of Contents

Description

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.

Table of Contents

1 Surface-knots.- 2 Knots.- 3 Motion pictures.- 4 Surface diagrams.- 5 Handle surgery and ribbon surface-knots.- 6 Spinning construction.- 7 Knot concordance.- 8 Quandles.- 9 Quandle homology groups and invariants.- 10 2-Dimensional braids.- Bibliography.- Epilogue.- Index.

by "Nielsen BookData"

Details

  • NCID
    BB27358356
  • ISBN
    • 9789811040900
  • Country Code
    si
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Singapore,[Germany]
  • Pages/Volumes
    xi, 212 p.
  • Size
    25 cm
  • Classification
  • Subject Headings
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