Surfaces in 4-Space [Hardcover]

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.

1 Diagrams of Knotted Surfaces.- 2 Constructions of Knotted Surfaces.- 3 Topological Invariants.- 4 Quandle Cocycle Invariants.- Epilogue.- Append.- References.

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 lÓd