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Science/Engineering Kevin Walker - An Extension of Casson's Invariant. (AM-126)

Posted on 2010-03-16




Name:Science/Engineering Kevin Walker - An Extension of Casson's Invariant. (AM-126)
ASIN/ISBN:0691025320
Language:English
File size:4.09 Mb
Publisher: Princeton University Press
Publish Date: 1992-03-03
ISBN: 0691025320
Pages: 150 pages
File Size: 4.09 MB
Other Info: DJVU
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Kevin Walker - 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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