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Lectures on the Topology of 3-Manifolds: An Introduction to the Casson Invariant (De Gruyter Textbook) - Hardcover
Synopsis
Progress in low-dimensional topology has been very fast over the last two decades, leading to the solutions of many difficult problems. One of the consequences of this "acceleration of history" is that many results have only appeared in professional journals and monographs. These are hardly accessible to students who have completed only a basic course in algebraic topology, or even to some researchers whose immediate area of expertise is not topology.
Among the highlights of this period are Casson’s results on the Rohlin invariant of homotopy 3-spheres, as well as his l-invariant. The purpose of this book is to provide a much-needed bridge to these modern topics. The book covers some classical topics, such as Heegaard splittings, Dehn surgery, and invariants of knots and links. It proceeds through the Kirby calculus and Rohlin’s theorem to Casson’s invariant and its applications, and gives a brief sketch of links with the latest developments in low-dimensional topology and gauge theory.
The book will be accessible to graduate students in mathematics and theoretical physics familiar with some elementary algebraic topology, including the fundamental group, basic homology theory, and Poncaré duality on manifolds.
"synopsis" may belong to another edition of this title.
- Publisherde Gruyter
- Publication date1999
- ISBN 10 3110162725
- ISBN 13 9783110162721
- BindingHardcover
- LanguageEnglish
- Number of pages199
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Buch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Frontmatter -- Preface -- Contents -- Introduction -- Glossary -- Lecture 1. Heegaard splittings -- Lecture 2. Dehn surgery -- Lecture 3. Kirby calculus -- Lecture 4. Even surgeries -- Lecture 5. Review of 4-manifolds -- Lecture 6. Four-manifolds with boundary -- Lecture 7. Invariants of knots and links -- Lecture 8. Fibered knots -- Lecture 9. The Arf-invariant -- Lecture 10. Rohlin's theorem -- Lecture 11. The Rohlin invariant -- Lecture 12. The Casson invariant -- Lecture 13. The group SU(2) -- Lecture 14. Representation spaces -- Lecture 15. The local properties of representation spaces -- Lecture 16. Casson's invariant for Heegaard splittings -- Lecture 17. Casson's invariant for knots -- Lecture 18. An application of the Casson invariant -- Lecture 19. The Casson invariant of Seifert manifolds -- Conclusion -- Exercises -- Bibliography -- Index 212 pp. Englisch. Seller Inventory # 9783110162721
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Buch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - Frontmatter -- Preface -- Contents -- Introduction -- Glossary -- Lecture 1. Heegaard splittings -- Lecture 2. Dehn surgery -- Lecture 3. Kirby calculus -- Lecture 4. Even surgeries -- Lecture 5. Review of 4-manifolds -- Lecture 6. Four-manifolds with boundary -- Lecture 7. Invariants of knots and links -- Lecture 8. Fibered knots -- Lecture 9. The Arf-invariant -- Lecture 10. Rohlin's theorem -- Lecture 11. The Rohlin invariant -- Lecture 12. The Casson invariant -- Lecture 13. The group SU(2) -- Lecture 14. Representation spaces -- Lecture 15. The local properties of representation spaces -- Lecture 16. Casson's invariant for Heegaard splittings -- Lecture 17. Casson's invariant for knots -- Lecture 18. An application of the Casson invariant -- Lecture 19. The Casson invariant of Seifert manifolds -- Conclusion -- Exercises -- Bibliography -- Index. Seller Inventory # 9783110162721
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