Existence of Borromean links in real entangled polymer systems

Determine whether entangled polymer solutions, kinetoplast DNA networks, and DNA-based Olympic hydrogels contain Borromean links, i.e., three-component links in which no pair of components is directly Hopf-linked.

Background

Borromean links are three-component links where no two components are directly linked, requiring three-body invariants to detect. Although simulations have hinted at their formation in dense polymer systems, experimental evidence remains elusive due to the computational difficulty of triple link invariants and the complexity of three-chain interactions.

The paper motivates a minimal geometric model (random rectangles) to explore whether such Borromean connectivity could plausibly emerge in dense, disordered environments analogous to ring-polymer solutions, kinetoplast DNA, and DNA-based Olympic gels.