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Lectures on the topology of 3-manifolds : an introduction to the Casson invariant

Author: Nikolai Saveliev
Publisher: Berlin ; New York : Walter de Gruyter, 1999.
Series: De Gruyter textbook.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
Summary:
"Progress in low-dimensional topology has been very fast in the last two decades, leading to the solutions of many difficult problems." "Among the highlights of this period are Casson's results on the Rohlin invariant of homotopy 3-spheres, as well as his [lambda]-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  Read more...
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Document Type: Book
All Authors / Contributors: Nikolai Saveliev
ISBN: 3110162725 9783110162721 3110162717 9783110162714
OCLC Number: 41967193
Description: ix, 199 pages : illustrations ; 25 cm.
Contents: 1. Heegaard splittings --
2. Dehn surgery --
3. Kirby calculus --
4. Even surgeries --
5. Review of 4-manifolds --
6. Four-manifolds with boundary --
7. Invariants of knots and links --
8. Fibered knots --
9. The Arf-invariant --
10. Rohlin's theorem --
11. The Rohlin invariant --
12. The Casson invariant --
13. The group SU(2) --
14. Representation spaces --
15. The local properties of representation spaces --
16. Casson's invariant for Heegaard splittings --
17. Casson's invariant for knots --
18. An application of the Casson invariant --
19. The Casson invariant of Seifert manifolds.
Series Title: De Gruyter textbook.
Responsibility: Nikolaĭ Saveliev.
More information:

Abstract:

"Progress in low-dimensional topology has been very fast in the last two decades, leading to the solutions of many difficult problems." "Among the highlights of this period are Casson's results on the Rohlin invariant of homotopy 3-spheres, as well as his [lambda]-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 text 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 Poincare duality on manifolds."--Jacket.

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