Knots and surfaces
著者
書誌事項
Knots and surfaces
Oxford University Press, 1994
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内容説明・目次
内容説明
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, this book takes the reader through recent advances in the 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.
目次
- Knots, links and diagrams
- knot and link polynomials
- topological spaces
- surfaces
- the arithmetic of knots
- presentations of groups
- graphs and trees
- Alexander's matrices and Alexander polynomials
- the fundamental group
- Van Kampen's theorem
- applications of Van Kampen's theorem
- covering spaces.
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