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

Kamada, Seiichi

doi:10.1090/S0002-9939-99-04924-2

Vanishing of a certain kind of Vassiliev invariants of 2-knots
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Proc. Amer. Math. Soc. 127 (1999), 3421-3426 Request permission

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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