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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A formula for Casson's invariant


Author: Jim Hoste
Journal: Trans. Amer. Math. Soc. 297 (1986), 547-562
MSC: Primary 57M25; Secondary 57N10
MathSciNet review: 854084
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Abstract: Suppose $ H$ is a homology $ 3$-sphere obtained by Dehn surgery on a link $ L$ in a homology $ 3$-sphere $ M$. If every pair of components of $ L$ has zero linking number in $ M$, then we give a formula for the Casson invariant, $ \lambda (H)$, in terms of $ \lambda (M)$, the surgery coefficients of $ L$, and a certain coefficient from each of the Conway polynomials of $ L$ and all its sublinks. A few consequences of this formula are given.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1986-0854084-4
PII: S 0002-9947(1986)0854084-4
Article copyright: © Copyright 1986 American Mathematical Society