Nikolai Saveliev

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

An Introduction to the Casson Invariant

• Format: PDF

Produktbeschreibung

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

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Produktdetails

• Verlag: De Gruyter
• Erscheinungstermin: 25. Oktober 2012
• Englisch
• ISBN-13: 9783110806359
• Artikelnr.: 53139237

Autorenporträt

Nikolai Saveliev, Department of Mathematics, Tulane University, New Orleans, 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

Rezensionen

"This is an excellent introduction to the Rokhlin and Casson invariants for homology 3-spheres [...], and in particular also to the necessary background material from the theory of 3- and 4-manifolds [...], so the book may serve also as a reasonable short and efficient introduction to some important parts of low-dimensional topology. It grew out of a course for second year graduate students and concentrates 19 lectures on less than 200 pages, including also a glossary on back-ground material from algebraic topology, a collection of exercises, open problems and comments on recent developments [...] To conclude, the author has succeeded in presenting a lot of material in a clear and efficient way, and the book is interesting and stimulating to read."
Birge Zimmermann-Huisgen, Zentralblatt MATH