ENGLISH

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

Book information

Publisher
Princeton University Press
Year
2016
ISBN
9781400882465
DOI
10.1515/9781400882465
Language
english
Format
PDF
Filesize
4 MB (4570535 bytes)
Series
Annals of Mathematics Studies; 126
Pages
150\139
Library
degruyter.com
Time added
2023-08-23 23:15:54

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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