Abstract

The paper constructs an example of a (non-ambient) isotopy of a (topological) knot in [Formula: see text] which does not extend to an isotopy of a two-component link whose second component is a meridianal ring of this knot. By constructing the example, the paper answers a question raised in 2005 by Melikhov. Apart from presenting the corresponding example, the paper will discuss the consequences that the discovery of this example has for attacking a problem that was in literature asked in 1974 by Rolfsen: Namely deciding, whether there exist knots (and it is clear that at most everywhere wild knots might have such a property) that even with respect to ordinary (not necessarily ambient) isotopy are non-equivalent to the trivial knot.

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