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Homology of weighted simplicial complexes. (English) Zbl 0735.18011

The author generalizes the notion of a simplicial complex to that of a weighted simplicial complex. He then constructs an ”integral” homology functor \(H\) defined on this category and proves that, with a suitable notion of contiguity, \(H\) satisfies the Eilenberg-Steenrod axioms. He further shows that \(H\) differs from homology for standard simplicial complexes by providing a simple example for which the positive- dimensional homology is zero but which has torsion in dimension zero. He explains the apparent paradox in categorical terms. Finally he applies his constructions to provide a homology functor on the category of preconvexity spaces.

MSC:

18G30 Simplicial sets; simplicial objects in a category (MSC2010)
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References:

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