On the homology of locally finite graphs

Details On the homology of locally finite graphs On the homology of locally finite graphs

2009-10-29

arxiv.org/abs/0910.5634v1

Mathematics

Combinatorics

30 pages. This is an extended version of the paper "The homology of a locally finite graph with ends" (to appear in Combinator

Scientific paper

We show that the topological cycle space of a locally finite graph is a canonical quotient of the first singular homology group of its Freudenthal compactification, and we characterize the graphs for which the two coincide. We construct a new singular-type homology for non-compact spaces with ends, which in dimension~1 captures precisely the topological cycle space of graphs but works in any dimension.

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