Topological chirality nonoriented links

Figure 31. (a) Minimal diagram of the simplest topologically chiral, nonoriented link, 4i. (b) The... 

With few exceptions, all nonoriented chemical links reported in the literature are topologically achiral. One of the rare exceptions is the two-component 4-crossing link 4 (Figure 31).114 The molecule in the depicted conformation, and indeed in any imaginable conformation, is geometrically chiral. It is therefore reasonable to conjecture that it is also topologically chiral. Proof that 4 is indeed topologically chiral was provided after the development of suitable polynomials.115... 

While orientation normally imparts topological chirality, as in the case of the Hopf link, this is not always the case. For example, the Borromean link remains amphicheiral even after orientation.115- 119 This is easily demonstrated with reference to the 5), presentation of the nonoriented link [Figure 27(b)] No matter in which direction the three rings are oriented, the resulting diagram remains centrosymmetric and therefore rigidly achiral. 

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