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Abstract
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We consider surgery moves along
–component
Brunnian links in compact connected oriented
–manifolds, where the framing
of the components is in .
We show that no finite type invariant of degree
can
detect such a surgery move. The case of two link-homotopic Brunnian links is also
considered. We relate finite type invariants of integral homology spheres
obtained by such operations to Goussarov–Vassiliev invariants of Brunnian
links.
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Keywords
3-manifolds, finite type invariants, Brunnian links,
Goussarov-Vassiliev invariants, claspers
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Mathematical Subject Classification 2000
Primary: 57N10
Secondary: 57M27
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Publication
Received: 30 May 2006
Accepted: 14 November 2006
Published: 13 December 2006
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