Shellability and Regularity of Chain Complexes over a Principal Ring

Details Shellability and Regularity of Chain Complexes over a Principal Ring Shellability and Regularity of Chain Complexes over a Principal Ring

2011-12-20

arxiv.org/abs/1112.4668v1

Mathematics

Algebraic Topology

24 pages

Scientific paper

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 topological invariant. In particular, we study special chain complexes, which are cones, and a class of regular chain complexes, for which shellability yields complete homological information.

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