An extension of Casson's invariant
Kevin Walker
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
种类:
年:
1992
出版社:
Princeton University Press
语言:
english
ISBN 10:
0691087660
ISBN 13:
9780691087665
系列:
Annals of mathematics studies, no. 126
文件:
DJVU, 2.12 MB
IPFS:
,
english, 1992
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