Mathematics Colloquia and Seminars

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A Brunnian link is a link, L, of n components (n >2) such that L is not the unlink, but every sublink is an unlink. The most famous Brunnian link is the Borromean Rings. Mike Freedman and Richard Skora proved in 1987 that no Brunnian link can be made out of round circles. We look at two generalizations of this theorem. The first generalization asks, what if instead of requiring the components of the link to be round circles, we only require them to convex planar regions? We will show that the Borromean rings are the unique Brunnian links of three or four components that can be formed under these regions? We will show that the Borromean rings are the unique Brunnian links of three or four components that can be formed under these conditions. The second question we ask is what happens if we look at linked spheres in higher dimensions.