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portada An Extension of Casson's Invariant. (Am-126)
Type
Physical Book
Publisher
Author
Year
1992
Language
English
Pages
140
Format
Paperback
ISBN
0691025320
ISBN13
9780691025322
Categories

An Extension of Casson's Invariant. (Am-126)

Kevin Walker (Author) · Princeton University Press · Paperback

An Extension of Casson's Invariant. (Am-126) - Kevin Walker

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Synopsis "An Extension of Casson's Invariant. (Am-126) "

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.

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