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Cords and 1-handles attached to surface-knots

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Abstract

Boyle classified 1-handles attached to surface-knots, that are closed and connected surfaces embedded in the Euclidean \(4\)-space, in the case that the surfaces are oriented and 1-handles are orientable with respect to the orientations of the surfaces. In that case, the equivalence classes of 1-handles correspond to the equivalence classes of cords attached to the surface-knot, and correspond to the double cosets of the peripheral subgroup of the knot group. In this paper, we classify cords and cords with local orientations attached to (possibly non-orientable) surface-knots. And we classify 1-handles attached to surface-knots in the case that the surface-knots are oriented and 1-handles are non-orientable, and in the case that the surface-knots are non-orientable.

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Authors and Affiliations

  1. Department of Mathematics, Osaka City University, Sumiyoshi, Osaka, 558-8585, Japan

    Seiichi Kamada

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  1. Seiichi Kamada
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Correspondence to Seiichi Kamada.

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   Dedicated to Fico González-Acuña on his 70th birthday.

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Kamada, S. Cords and 1-handles attached to surface-knots. Bol. Soc. Mat. Mex. 20, 595–609 (2014). https://doi.org/10.1007/s40590-014-0022-x

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  • DOI: https://doi.org/10.1007/s40590-014-0022-x

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