An Extension of Casson's Invariant. (AM-126), Volume 126

(Paperback)

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This monograph describes an invariant, lambda, of oriented rational homology 3-spheres, which is a generalization of Andrew Casson's work in the integer homology sphere case. A formula describing how lambda transforms under Dehn surgery is provided. The formula involves Alexander polynomials and Dedekind sums, and can be used to give a rather elementary proof of the existence of lambda. It is also shown that when M is a Z2-homology sphere, lambda (M) determines the Rochlin invariant of M.

Reviews

"[This is] a monograph describing Walker's extension of Casson's invariant to Q HS ... This is a fascinating subject and Walker's book is informative and well written ... it makes a rather pleasant introduction to a very active area in geometric topology."--Bulletin of the American Mathematical Society