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Das Zentralarchiv für Mathematiker-Nachlässe Grenzebach, Gerrit; Habermann, Katharina
Mitteilungen der Deutschen Mathematiker-Vereinigung,
7/2016, Letnik:
24, Številka:
2
Journal Article
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, which we call
totally regular
, for which we can obtain complete homological information if an additional condition is fulfilled.
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.
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