  Scattering theory for p-forms on manifolds with cylindrical ends has a direct
interpretation in terms of cohomology. Using the Hodge isomorphism,the
scattering matrix at low energy may be regarded as operator on the cohomology
of the boundary. Its value at zero describes the image of the absolute
cohomology in the cohomology of the boundary. We show that the so-called
scattering length, the Eisenbud-Wigner time delay at zero energy, has a
cohomological interpretation as well. Namely, it relates the norm of a
cohomology class on the boundary to the norm of its image under the connecting
homomorphism in the long exact sequence in cohomology. An interesting
consequence of this is that one can estimate the scattering lengths in terms of
geometric data like the volumes of certain homological systoles.
