Brunnian links, claspers and Goussarov–Vassiliev finite type invariants
2007 ◽
Vol 142
(3)
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pp. 459-468
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AbstractGoussarov and the author independently proved that two knots in S3 have the same values of finite type invariants of degree <n if and only if they are Cn-equivalent, which means that they are equivalent up to modification by a kind of geometric commutator of class n. This property does not generalize to links with more than one component.In this paper, we study the case of Brunnian links, which are links whose proper sublinks are trivial. We prove that if n ≥ 1, then an (n+1)-component Brunnian link L is Cn-equivalent to an unlink. We also prove that if n ≥ 2, then L can not be distinguished from an unlink by any Goussarov–Vassiliev finite type invariant of degree <2n.
2008 ◽
Vol 19
(06)
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pp. 747-766
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2013 ◽
Vol 22
(08)
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pp. 1350042
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2004 ◽
Vol 13
(01)
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pp. 1-11
2006 ◽
Vol 15
(09)
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pp. 1163-1199
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2000 ◽
Vol 09
(06)
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pp. 735-758
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2013 ◽
Vol 22
(08)
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pp. 1350037
1996 ◽
Vol 05
(04)
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pp. 441-461
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Keyword(s):
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