  Taking the l^1-completion and the topological dual of the singular chain
complex gives rise to l^1-homology and bounded cohomology respectively. In
contrast to l^1-homology, major structural properties of bounded cohomology are
well understood by the work of Gromov and Ivanov.
  Based on an observation by Matsumoto and Morita, we derive a mechanism
linking isomorphisms on the level of homology of Banach chain complexes to
isomorphisms on the level of cohomology of the dual Banach cochain complexes
and vice versa. Therefore, certain results on bounded cohomology can be
transferred to l^1-homology. For example, we obtain a new proof of the fact
that l^1-homology depends only on the fundamental group and that l^1-homology
with twisted coefficients admits a description in terms of projective
resolutions. The latter one in particular fills a gap in Park's approach.
  In the second part, we demonstrate how l^1-homology can be used to get a
better understanding of simplicial volume of non-compact manifolds.
