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Title: AN EXTENSION OF CASSON'S INVARIANT. (AM-126), VOLUME 126
By: Kevin Walker
Format: Paperback

List price: £62.00
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ISBN 10: 0691025320
ISBN 13: 9780691025322
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Publisher: PRINCETON UNIVERSITY PRESS
Pub. date: 3 March, 1992
Series: Annals of Mathematics Studies 126
Pages: 150
Description: 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.
Synopsis: 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.
Publication: US
Imprint: Princeton University Press
Returns: Returnable
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