  Molecular dynamics simulations confirm recent extensional flow experiments
showing ring polymer melts exhibit strong extension-rate thickening of the
viscosity at Weissenberg numbers $Wi<<1$. Thickening coincides with the extreme
elongation of a minority population of rings that grows with $Wi$. The large
susceptibility of some rings to extend is due to a flow-driven formation of
topological links that connect multiple rings into supramolecular chains. Links
form spontaneously with a longer delay at lower $Wi$ and are pulled tight and
stabilized by the flow. Once linked, these composite objects experience larger
drag forces than individual rings, driving their strong elongation. The
fraction of linked rings generated by flow depends non-monotonically on $Wi$,
increasing to a maximum when $Wi\sim1$ before rapidly decreasing when the
strain rate approaches the relaxation rate of the smallest ring loops $\sim
1/\tau_e$.
