The main theme of this book is the mathematical theory of knots and its interaction with the theory of surfaces and of group presentations.
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.
Topics 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, this book presents novel challenges to students and other interested readers.
By:
Gilbert,
Porter
Imprint: Oxford University Press
Country of Publication: United Kingdom
Edition: New edition
Dimensions:
Height: 234mm,
Width: 156mm,
Spine: 16mm
Weight: 443g
ISBN: 9780198514909
ISBN 10: 0198514905
Pages: 280
Publication Date: 22 February 1996
Audience:
College/higher education
,
Primary
Format: Paperback
Publisher's Status: Active
1: Knots, Links, and Diagrams 2: Knot and Link Polynomials 3: Topological Spaces 4: Surfaces 5: The Arithmetic of Knots 6: Presentations of Groups 7: Graphs and Trees 8: Alexanders Matrices and Alexander Polynomials 9: The Fundamental Group 10: Van Kampen's Theorem 11: Applications of Van Kampen Theorem 12: Covering Spaces Bibliography Index
Reviews for Knots and Surfaces
<br> This excellent book is based....on a third-year undergraduate course....The authors have been successful in giving as much motivation as possible for each of the notions considered in the book. --Mathematical Reviews<p><br>
