Band-pass moves and the Casson-Walker-Lescop invariant (Q1774343)
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scientific article; zbMATH DE number 2166324
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Band-pass moves and the Casson-Walker-Lescop invariant |
scientific article; zbMATH DE number 2166324 |
Statements
Band-pass moves and the Casson-Walker-Lescop invariant (English)
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9 May 2005
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In 1985, Casson introduced the invariant of integral homology spheres which now bears his name, see for example [\textit{S. Akbulut and J. McCarthy}, Casson's invariant for oriented homology 3-spheres, An exposition, Mathematical Notes 36, (Princeton Univesity Press, Princeton) (1990; Zbl 0695.57011)]. Soon thereafter Walker extended this invariant to rational homology spheres in [\textit{K. Walker}, An extension of Casson's invariant, Annals of Mathematics Studies 126, (Princeton University Press, Princeton) (1992; Zbl 0752.57011)]. Both Casson and Walker gave surgery formulae for the invariant -- i.e. formulae showing how the invariant changes under Dehn surgery on a knot in an integral (resp. rational) homology sphere. In a previous paper [\textit{J. Johannes}, J. Knot Theory Ramifications 8, No. 4, 491--504 (1999; Zbl 0940.57019)], the author of the paper under review derived a formula for the difference in the Casson-Walker invariants of two 3-manifolds obtained by surgery on links which differ by a crossing change in one component of the link. Here, he investigates the same problem, now allowing crossing changes between components of the link effected by band-pass moves.
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Casson-Walker invariant
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homology spheres
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surgery formulae
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