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.
Additional ISBNs
9780691087665, 9780691025322, 0691087660, 0691025320, 9780691025322
An Extension of Casson?s Invariant. (AM-126), Volume 126 Ebook
By: Kevin Walker
Publisher:
Princeton University Press
Print ISBN: 9780691087665, 0691087660
eText ISBN: 9781400882465, 140088246X
Copyright year: 1992
Format: PDF
Available from $ 67.50 USD
SKU: 9781400882465
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