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

Walker, Kevin

 
9780691025322: An Extension of Casson's Invariant. (AM-126)
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ISBN 10: 0691025320 ISBN 13: 9780691025322
Publisher: Princeton University Press, 1992
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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.

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Review:
"[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)

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  • PublisherPrinceton University Press
  • Publication date1992
  • ISBN 10 0691025320
  • ISBN 13 9780691025322
  • BindingPaperback
  • Number of pages150

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