An Extension of Casson's Invariant. (AM-126) (Annals of Mathematics Studies, 126) - Image 1

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Princeton University Press An Extension of Casson's Invariant. (AM-126) (Annals of Mathematics Studies, 126)

Name: An Extension of Casson's Invariant. (AM-126) (Annals of Mathematics Studies, 126)
Brand: Princeton University Press
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Algebra

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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.

Product Specifications

Brand: Princeton University Press
Format: paperback
ASIN: 0691025320
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Algebra
Domain: Amazon UK
Publication Date: 23 March 1992
Listed Since: 16 December 2006

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Princeton University Press An Extension of Casson's Invariant. (AM-126) (Annals of Mathematics Studies, 126)

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