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Duality in Infinite Graphs

Published online by Cambridge University Press:  03 January 2006

HENNING BRUHN  and
REINHARD DIESTEL
HENNING BRUHN
Affiliation:
Mathematisches Seminar, Universität Hamburg, Bundesstraße 55, 20146 Hamburg, Germany (e-mail: hbruhn@gmx.net, diestel@math.uni-hamburg.de)
REINHARD DIESTEL
Affiliation:
Mathematisches Seminar, Universität Hamburg, Bundesstraße 55, 20146 Hamburg, Germany (e-mail: hbruhn@gmx.net, diestel@math.uni-hamburg.de)
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Abstract

The adaption of combinatorial duality to infinite graphs has been hampered by the fact that while cuts (or cocycles) can be infinite, cycles are finite. We show that these 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. Our approach enables us to complete Thomassen's results about ‘finitary’ duality for infinite graphs to full duality, including his extensions of Whitney's theorem.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 15 , Issue 1-2 , January 2006 , pp. 75 - 90
Copyright
2006 Cambridge University Press

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