# On the homology of locally compact spaces with ends

@article{Diestel2009OnTH,
title={On the homology of locally compact spaces with ends},
author={Reinhard Diestel and Philipp Sprussel},
journal={Topology and its Applications},
year={2009},
volume={158},
pages={1626-1639}
}
• Published 29 October 2009
• Mathematics, Computer Science
• Topology and its Applications
8 Citations

## Figures from this paper

The fundamental group of a locally finite graph with ends: a hyperfinite approach
• Mathematics
• 2012
The end compactification |\Gamma| of the locally finite graph \Gamma is the union of the graph and its ends, endowed with a suitable topology. We show that \pi_1(|\Gamma|) embeds into a nonstandard
On the coincidence of zeroth Milnor-Thurston homology with singular homology
• Mathematics
• 2014
In this paper we prove that the zeroth Milnor-Thurston homology group coincides with singular homology for Peano Continua. More- over, we show that the canonical homomorphism between these ho- mology
Labeled Trees Generating Complete, Compact, and Discrete Ultrametric Spaces
• Mathematics
Annals of Combinatorics
• 2022
We investigate the interrelations between labeled trees and ultrametric spaces generated by these trees. The labeled trees, which generate complete ultrametrics, totally bounded ultrametrics, and

## References

SHOWING 1-10 OF 25 REFERENCES
The homology of locally finite graphs with ends
• Mathematics
• 2008
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
The homology of a locally finite graph with ends
• Mathematics
Comb.
• 2010
A new singular-type homology for non-compact spaces with ends is constructed, which in dimension 1 captures precisely the topological cycle space of graphs but works in any dimension.
The Cycle Space of an Infinite Graph
• R. Diestel
• Mathematics
Combinatorics, Probability and Computing
• 2005
A new ‘singular’ approach is presented that builds the cycle space of a graph not on its finite cycles but on its topological circles, the homeomorphic images of $S^1$ in the space formed by the graph together with its ends.
Duality in Infinite Graphs
• Mathematics
Combinatorics, Probability and Computing
• 2006
This work shows that obstructions fall away when duality is reinterpreted on the basis of a ‘singular’ approach to graph homology, whose cycles are defined topologically in a space formed by the graph together with its ends and can be infinite.
On Infinite Cycles I
• Mathematics
Comb.
• 2004
We adapt the cycle space of a finite graph to locally finite infinite graphs, using as infinite cycles the homeomorphic images of the unit circle S1 in the graph compactified by its ends. We prove
Eulerian edge sets in locally finite graphs
• Mathematics
Comb.
• 2011
In a finite graph, an edge set Z is an element of the cycle space if and only if every vertex has even degree in Z. We extend this basic result to the topological cycle space, which allows infinite
Cycle‐cocycle partitions and faithful cycle covers for locally finite graphs
• Mathematics
J. Graph Theory
• 2005
It is shown that if Seymour’s faithful cycle cover conjecture is true for finite graphs then it also holds for locally finite graphs when infinite cyles are allowed in the cover, but not otherwise.
Geodetic Topological Cycles in Locally Finite Graphs
• Mathematics
Electron. J. Comb.
• 2009
We prove that the topological cycle space C(G) of a locally finite graph G is generated by its geodetic topological circles. We further show that, although the finite cycles of G generate C(G), its