  We present a novel mechanism for resolving the mechanical rigidity of
nanoscopic circular polymers that flow in a complex environment. The emergence
of a regime of negative differential mobility induced by topological
interactions between the rings and the substrate is the key mechanism for
selective sieving of circular polymers with distinct flexibilities. A simple
model accurately describes the sieving process observed in molecular dynamics
simulations and yields experimentally verifiable analytical predictions, which
can be used as a reference guide for improving filtration procedures of
circular filaments. The topological sieving mechanism we propose ought to be
relevant also in probing the microscopic details of complex substrates.
