Geodesic
Some Counterexamples in Link Theory
Canadian journal of mathematics, Tome 26 (1974) no. 4, pp. 978-984

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This note is concerned specifically with links of two (disjoint) n-spheres in an (n + 2)-manifold M, i.e. embeddings L:Sn + Sn —> M. The links L 0 and L 1 are isotopic if they are t he ends of a continuous family Li :Sn + Sn —> M (0 ≦ t ≦ 1) of links. They are ambient isotopic or equivalent if there is a continuous family of self-homeomorphisms ht : M—> M (0 ≦ t ≦ 1) such that h 0 = identity and h 1◯L0 = L1. Ambient isotopic links are isotopic, but not conversely. For example, an isotopy can tie and untie little knots (as in Figure 3) in the components of a link, thus changing the original link into one which is inequivalent to the original. 
Rolfsen, Dale. Some Counterexamples in Link Theory. Canadian journal of mathematics, Tome 26 (1974) no. 4, pp. 978-984. doi: 10.4153/CJM-1974-091-6
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