  The goal of this paper is to generalize some of the existing toolkit of
combinatorial algebraic topology in order to study the homology of abstract
chain complexes. We define shellability of chain complexes in a similar way as
for cell complexes and introduce the notion of regular chain complexes. In the
case of chain complexes coming from simplicial complexes we recover the
classical notions but, in contrast to the topological case, in the abstract
setting shellings turn out to be a weaker homological invariant. In particular,
we study special chain complexes, which are cones, and a class of regular chain
complexes, for which we can obtain complete homological information.
