An Extension of Casson's Invariant. (AM-126) - Kevin Walker (1992)
ISBN 0691025320
Subject Invariants; Three-manifolds (Topology)
Publisher Princeton University Press
Publication Date 3/3/1992
Format Paperback (230 x 152 mm)
Language e

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.

Personal Details
Collection Status In Collection
Index 178
Read It Yes
Links Amazon US
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Product Details
LoC Classification QA613 .W34 1992
Dewey 514/.3
Cover Price $41.00
No. of Pages 150