The homology of a locally finite graph with ends

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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Correspondence to Reinhard Diestel.

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

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Mathematics Subject Classification (2000)

  • 05C63
  • 55N10