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… (More)

@article{Diestel2010TheHO,
title={The homology of a locally finite graph with ends},
author={Reinhard Diestel and Philipp Spr{\"u}ssel},
journal={Combinatorica},
year={2010},
volume={30},
pages={681-714}
}