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"Even" Borromean links

Next, we could try to construct Borromean links with an even number of components and without the Brunnian property. C. Liang and K. Mislow [8] proposed two methods for the construction of n-Borromean links with at least one nontrivial sublink, by but they both result in n-Borromean links with some nonintersecting component projections (n>3). In the first method, involving duplication of one or more rings, the duplicate rings are interchangeable by continuous deformation. For example, by duplicating one ring in Borromean rings, we obtain 4-Borromean link, and continuing in the same manner, n-Borromean links (n=5,6,7). Different links of that infinite series follow from other choices of rings that will be duplicated.


Another method is similar to the one for producing "fractal" Borromean rings: in the trivial link, two crossing points are surrounded by nonintersecting circles. Continuing in this way, Borromean links with an even number of components are obtained.


Finaly, only one open question remains: are they exist (2n)-Borromean links in which every pair of component projections has a crossing in all projections of the link, and moreover, where all components are equivalent.


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