An Extension of Casson's Invariant
Extension of Casson's Invariant. (AM-126), Volume 126
1st Edition
Published on 6. June 2016
150 pages
978-1-4008-8246-5 (ISBN)
Description
This book describes an invariant, l, of oriented rational homology 3-spheres which is a generalization of work of Andrew Casson in the integer homology sphere case. Let R(X) denote the space of conjugacy classes of representations of p(X) into SU(2). Let (W,W,F) be a Heegaard splitting of a rational homology sphere M. Then l(M) is declared to be an appropriately defined intersection number of R(W) and R(W) inside R(F). The definition of this intersection number is a delicate task, as the spaces involved have singularities.
A formula describing how l transforms under Dehn surgery is proved. The formula involves Alexander polynomials and Dedekind sums, and can be used to give a rather elementary proof of the existence of l. It is also shown that when M is a Z-homology sphere, l(M) determines the Rochlin invariant of M.
A formula describing how l transforms under Dehn surgery is proved. The formula involves Alexander polynomials and Dedekind sums, and can be used to give a rather elementary proof of the existence of l. It is also shown that when M is a Z-homology sphere, l(M) determines the Rochlin invariant of M.
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03/1992
Princeton University Press
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Kevin Walker
An Extension of Casson's Invariant
Book
03/1992
Princeton University Press
€105.23
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Person
Kevin Walker
Content
- Frontmatter,
- Contents,
- 0. Introduction,
- 1. Topology of Representation Spaces,
- 2. Definition of ¿,
- 3. Various Properties of ¿,
- 4. The Dehn Surgery Formula,
- 5. Combinatorial Definition of ¿,
- 6. Consequences of the Dehn Surgery Formula,
- A. Dedekind Sums,
- B. Alexander Polynomials,
- Bibliography,
