Nikolai Saveliev

Lectures on the Topology of 3-Manifolds (eBook, PDF)

An Introduction to the Casson Invariant

• Format: PDF

Produktbeschreibung

This textbook, now in its second revised and extended edition, introduces the topology of 3- and 4-dimensional manifolds. It also considers new developments especially related to the Heegaard Floer and contact homology. The book is accessible to graduate students in mathematics and theoretical physics familiar with some elementary algebraic topology, including the fundamental group, basic homology theory, and Poincaré duality on manifolds.

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Produktdetails

• Verlag: Walter de Gruyter
• Seitenzahl: 218
• Erscheinungstermin: 23. Dezember 2011
• Englisch
• ISBN-13: 9783110250367
• Artikelnr.: 48598426

Autorenporträt

Nikolai Saveliev, University of Miami, Florida, USA.

Inhaltsangabe

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