  We consider forces acting on objects immersed in, or attached to, long
fluctuating polymers. The confinement of the polymer by the obstacles results
in polymer-mediated forces that can be repulsive (due to loss of entropy) or
attractive (if some or all surfaces are covered by adsorbing layers). The
strength and sign of the force in general depends on the detailed shape and
adsorption properties of the obstacles, but assumes simple universal forms if
characteristic length scales associated with the objects are large. This occurs
for scale-free shapes (such as a flat plate, straight wire, or cone), when the
polymer is repelled by the obstacles, or is marginally attracted to it (close
to the depinning transition where the absorption length is infinite). In such
cases, the separation $h$ between obstacles is the only relevant macroscopic
length scale, and the polymer mediated force equals ${\cal A} \, k_{B}T/h$,
where $T$ is temperature. The amplitude ${\cal A}$ is akin to a critical
exponent, depending only on geometry and universality of the polymer system.
The value of ${\cal A}$, which we compute for simple geometries and ideal
polymers, can be positive or negative. Remarkably, we find ${\cal A}=0$ for
ideal polymers at the adsorption transition point, irrespective of shapes of
the obstacles, i.e. at this special point there is no polymer-mediated force
between obstacles (scale-free or not).
