Knots and Surfaces
Seiten
1996
Oxford University Press (Verlag)
978-0-19-851490-9 (ISBN)
Oxford University Press (Verlag)
978-0-19-851490-9 (ISBN)
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.
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.
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.
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
| Erscheint lt. Verlag | 22.2.1996 |
|---|---|
| Zusatzinfo | line figures |
| Verlagsort | Oxford |
| Sprache | englisch |
| Maße | 156 x 234 mm |
| Gewicht | 443 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Angewandte Mathematik |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 0-19-851490-5 / 0198514905 |
| ISBN-13 | 978-0-19-851490-9 / 9780198514909 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
| Haben Sie eine Frage zum Produkt? |
Mehr entdecken
aus dem Bereich
aus dem Bereich
für Ingenieure und Naturwissenschaftler
Buch | Softcover (2024)
Springer Vieweg (Verlag)
CHF 48,95
Buch | Softcover (2025)
Springer Fachmedien Wiesbaden (Verlag)
CHF 69,95
Buch | Softcover (2024)
Springer Vieweg (Verlag)
CHF 62,95
