© 2004

Surfaces in 4-Space


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

  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

  • Book Title Surfaces in 4-Space
  • Authors Scott Carter
    Seiichi Kamada
    Masahico Saito
  • Series Title Encyclopaedia of Mathematical Sciences
  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2004
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-3-540-21040-5
  • Softcover ISBN 978-3-642-05913-1
  • eBook ISBN 978-3-662-10162-9
  • Series ISSN 0938-0396
  • Edition Number 1
  • Number of Pages XIII, 214
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Topology
  • Buy this book on publisher's site


From the reviews:

"The book … is devoted to the theory of knotted surfaces in R4 and possesses all the important features of a book which promises to become a classic. … The authors of the book are among the main founders of this theory and have contributed a great deal to its development. … the book may serve as a good introduction for a more or less experienced reader into the beautiful world of knotted surfaces."

Sergej V. Matveev, Mathematical Reviews, 2005e

"The book treats the theory of knotting of surfaces in 4-space presenting up to date results and research … . Each notion is precisely defined with a short historical account included. The results are gradually introduced, illustrated by examples, and original references are always cited. The reader is advised if a result has a higher dimensional counterpart. The book contains an exhaustive list of references and the index. It represents a nice, useful and reliable encyclopaedic presentation of the above mentioned subject … ."

Ivan Ivanšic, Zentralblatt MATH, Vol. 1078, 2006