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The homology of a locally finite graph with ends

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Abstract

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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  1. Mathematisches Seminar, Universität Hamburg, Bundesstraße 55, 20146, Hamburg, Germany

    Reinhard Diestel & Philipp Sprüssel

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  1. Reinhard Diestel
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  2. Philipp Sprüssel
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Correspondence to Reinhard Diestel.

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Diestel, R., Sprüssel, P. The homology of a locally finite graph with ends. Combinatorica 30, 681–714 (2010). https://doi.org/10.1007/s00493-010-2481-7

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