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

DOI:
https://doi.org/10.1090/S0002-9939-99-04924-2

Published electronically:
May 27, 1999

MathSciNet review:
1610788

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-99-04924-2

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