ENGLISH

An extension of Casson's invariant

By Kevin Walker

Book information

Publisher
Princeton University Press
Year
1992
ISBN
0691025320, 9780691025322
LCC
QA613 .W34 1992
Open Library ID
OL1560942M
Language
english
Format
DJVU
Filesize
4 MB (4286077 bytes)
Series
AM-126
Pages
133\133
Time added
2009-08-06 05:14:26

Description

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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