Read more
Zusatztext a virtually self-contained introduction .......... The text is very well written, detailed motivations of concepts and clear explanations replace unnecessary formalism. Recommended Klappentext 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. Zusammenfassung Knots and Surfaces is an account of the mathematical theory of knots and its interactions with related fields. This is an area of intense research activity, yet is accessible to the mathematics undergraduate. Throughout the book, mathematics is shown in action in a surprising and challenging way. Inhaltsverzeichnis 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
