Seiichi Kamada
Published 2014-03-04Version 1
J. 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.
Comments: It will appear in Boletin de la Sociedad Matematica Mexicana
The $ν^+$-equivalence classes of genus one knots
Sequences of knots and their limits
5-move equivalence classes of links and their algebraic invariants
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