Figure 1
From: Physical Links: defining and detecting inter-chain entanglement
Detection of physical links: The sketches illustrate a key step of the procedure, namely how a pair of open chains can be turned into rings by closing each of them with an auxiliary arc (thick dashed lines) pointing away from the centre of mass of the partner chain (filled circles). To minimize the additional entanglement that may arise during closure, the segments pointing away from the centre of mass of the other chain are typically chosen to be much longer than the radius of gyration of the chains. This closure “at infinity” turnes the two chains, Γ1 and Γ2, into the components, L 1 and L 2, of a proper link, whose topology can be established with suitable invariants, such as the multivariate Alexander polynomial. The procedure correctly distinguishes between the non-trivial entanglement in panel (a), a Solomon physical link, from the unlink of panel (b). The two link types are indicated, respectively, as \({4}_{1}^{2}\) and \({0}_{1}^{2}\) in the Rolfsen’s notation16.
