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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Vanishing of a certain kind
of Vassiliev invariants of 2-knots


Author: Seiichi Kamada
Journal: Proc. Amer. Math. Soc. 127 (1999), 3421-3426
MSC (1991): Primary 57Q45, 57M25
Published electronically: May 27, 1999
MathSciNet review: 1610788
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Abstract: In knot theory, Vassiliev's 1-knot invariants are defined in a combinatorial way as finite type invariants. By a natural generalization of the combinatorial definition, one has a certain family of 2-knot invariants, which should be called finite type 2-knot invariants. They form a subspace of the whole space of ``Vassiliev 2-knot invariants''. In this paper we prove that it is 1-dimensional.


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Additional Information

Seiichi Kamada
Affiliation: Department of Mathematics, Osaka City University, Sumiyoshi-ku, Osaka 558, Japan
Email: kamada@sci.osaka-cu.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04924-2
PII: S 0002-9939(99)04924-2
Keywords: 2-knot, Vassiliev invariant, finite type invariant, finger move, regular homotopy
Received by editor(s): May 22, 1997
Received by editor(s) in revised form: February 1, 1998
Published electronically: May 27, 1999
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 1999 American Mathematical Society