Knots and Surfaces

Paperback | April 30, 1999

byN. D. Gilbert, T. Porter

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Covering an area of current intense research interest, this book is ideal for all mathematicians, undergraduate or at research level, as an introduction to the field. The book provides a thorough account of the mathematical theory of knots and its interactions with related fields. This newpaperback edition places the book within reach of all individuals interested in this new and exciting field.

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From Our Editors

The main theme of this book is the mathematical theory of knots and its interaction with the theory of surfaces. Beginning with a simple diagrammatic approach to the study of knots, reflecting the artistic and geometric appeal of interlaced forms, Knots and Surfaces takes the reader through recent advances in our understanding to areas...

From the Publisher

Covering an area of current intense research interest, this book is ideal for all mathematicians, undergraduate or at research level, as an introduction to the field. The book provides a thorough account of the mathematical theory of knots and its interactions with related fields. This newpaperback edition places the book within reach ...

From the Jacket

The main theme of this book is the mathematical theory of knots and its interaction with the theory of surfaces. Beginning with a simple diagrammatic approach to the study of knots, reflecting the artistic and geometric appeal of interlaced forms, Knots and Surfaces takes the reader through recent advances in our understanding to areas...

N. D. Gilbert is at Heriot-Watt University, Edinburgh. T. Porter is at University of Wales at Bangor.

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Format:PaperbackDimensions:280 pages, 9.21 × 6.14 × 0.63 inPublished:April 30, 1999Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0198514905

ISBN - 13:9780198514909

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Table of Contents

1. Knots, Links, and Diagrams2. Knot and Link Polynomials3. Topological Spaces4. Surfaces5. The Arithmetic of Knots6. Presentations of Groups7. Graphs and Trees8. Alexanders Matrices and Alexander Polynomials9. The Fundamental Group10. Van Kampen's Theorem11. Applications of Van Kampen Theorem12. Covering SpacesBibliographyIndex

From Our Editors

The main theme of this book is the mathematical theory of knots and its interaction with the theory of surfaces. Beginning with a simple diagrammatic approach to the study of knots, reflecting the artistic and geometric appeal of interlaced forms, Knots and Surfaces takes the reader through recent advances in our understanding to areas of current research. Included are straightforward introductions to topological spaces, surfaces, the fundamental group, graphs, free groups, and group presentations. These topics combine into a coherent and highly developed theory to explore and explain the accessible and intuitive problems of knots and surfaces. Both as an introduction to several areas of prime importance to the development of pure mathematics today, and as an account of pure mathematics in action in an unusual context, the book presents novel challenges to students and other interested readers.

Editorial Reviews

`a virtually self-contained introduction .......... The text is very well written, detailed motivations of concepts and clear explanations replace unnecessary formalism. Recommended'Monatshefte fur Mathematik Vol. 124 1997