Surfaces in 4-Space

  • Scott Carter
  • Seiichi Kamada
  • Masahico Saito

Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 142)

Table of contents

  1. Front Matter
    Pages I-XIII
  2. Scott Carter, Seiichi Kamada, Masahico Saito
    Pages 1-39
  3. Scott Carter, Seiichi Kamada, Masahico Saito
    Pages 41-75
  4. Scott Carter, Seiichi Kamada, Masahico Saito
    Pages 77-121
  5. Scott Carter, Seiichi Kamada, Masahico Saito
    Pages 123-166
  6. Scott Carter, Seiichi Kamada, Masahico Saito
    Pages 167-167
  7. Back Matter
    Pages 169-213

About this book


Surfaces in 4-Space, written by leading specialists in the field, discusses knotted surfaces in 4-dimensional space and surveys many of the known results in the area. Results on knotted surface diagrams, constructions of knotted surfaces, classically defined invariants, and new invariants defined via quandle homology theory are presented. The last chapter comprises many recent results, and techniques for computation are presented. New tables of quandles with a few elements and the homology groups thereof are included.

This book contains many new illustrations of knotted surface diagrams. The reader of the book will become intimately aware of the subtleties in going from the classical case of knotted circles in 3-space to this higher dimensional case.

As a survey, the book is a guide book to the extensive literature on knotted surfaces and will become a useful reference for graduate students and researchers in mathematics and physics.


homology quandle rack homology surfaces topological invariant

Authors and affiliations

  • Scott Carter
    • 1
  • Seiichi Kamada
    • 2
  • Masahico Saito
    • 3
  1. 1.Department of Mathematics and StatisticsUniversity of South AlabamaMobileUSA
  2. 2.Department of MathematicsHiroshima UniversityHigashi-Hiroshima City, HiroshimaJapan
  3. 3.Department of MathematicsUniversity of South FloridaTampaUSA

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2004
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-05913-1
  • Online ISBN 978-3-662-10162-9
  • Series Print ISSN 0938-0396
  • Buy this book on publisher's site