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RIBBON KNOTS WITH TWO RIBBON TYPES
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A ribbon n-knot Kn is constructed by attaching m bands to m + 1n-spheres in the euclidean (n + 2)-space. There are many way of attaching them; as a result, Kn has many presentations which are called ribbon presentations. But concerning the case of m = 1, it was proved in the case of n = 1 by M. Scharlemann, and n ≥ 2 by Y. Marumoto that if Kn is unknotted, its ribbon presentation is essentially unique. In this note, we will prove in the case of m = 1 and n ≥ 2 that there are infinitely many ribbon n-knots which has essentially different two ribbon presentations.
Title: RIBBON KNOTS WITH TWO RIBBON TYPES
Description:
A ribbon n-knot Kn is constructed by attaching m bands to m + 1n-spheres in the euclidean (n + 2)-space.
There are many way of attaching them; as a result, Kn has many presentations which are called ribbon presentations.
But concerning the case of m = 1, it was proved in the case of n = 1 by M.
Scharlemann, and n ≥ 2 by Y.
Marumoto that if Kn is unknotted, its ribbon presentation is essentially unique.
In this note, we will prove in the case of m = 1 and n ≥ 2 that there are infinitely many ribbon n-knots which has essentially different two ribbon presentations.
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