  The impact of impenetrable obstacles on the energetics and equilibrium
structure of strongly repulsive directed polymers is investigated. As a result
of the strong interactions, regions of severe polymer depletion and excess are
found in the vicinity of the obstacle, and the associated free-energy cost is
found to scale quadratically with the average polymer density. The
polymer-polymer interactions are accounted for via a sequence of
transformations: from the 3D line liquid to a 2D fluid of Bose particles to a
2D composite fermion fluid and, finally, to a 2D one-component plasma. The
results presented here are applicable to a range of systems consisting of
noncrossing directed lines.
