An Extension of Casson's Invariant. (AM-126)
( Annals of Mathematics Studies )
Publication series ：Annals of Mathematics Studies
Author： Walker Kevin
Publisher： Princeton University Press
Publication year： 2016
E-ISBN: 9781400882465
P-ISBN(Paperback): 9780691025322
Subject： O189.3 analytical topology
Keyword： 拓扑（形势几何学）,数学
Language： ENG
Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.
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.
Chapter