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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
An Extension of Casson's Invariant. (Am-126), Volume 126

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

Walker, Kevin

Paperback

Series: Annals of Mathematics Studies, Book 126

General MathematicsGeneral Science

ISBN10: 0691025320
ISBN13: 9780691025322
Publisher: Princeton Univ Pr
Published: Mar 23 1992
Pages: 150
Weight: 0.48
Height: 0.39 Width: 6.17 Depth: 9.25
Language: English

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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