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Cycle decompositions : from graphs to continua
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Georgakopoulos, Agelos (2012) Cycle decompositions : from graphs to continua. Advances in Mathematics, Vol.229 (No.2). pp. 935-967. doi:10.1016/j.aim.2011.10.015 ISSN 0001-8708.
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Official URL: http://dx.doi.org/10.1016/j.aim.2011.10.015
Abstract
We generalise a fundamental graph-theoretical fact, stating that every element of the cycle space of a graph is a sum of edge-disjoint cycles, to arbitrary continua. To achieve this we replace graph cycles by topological circles, and replace the cycle space of a graph by a new homology group for continua which is a quotient of the first singular homology group H1. This homology seems to be particularly apt for studying spaces with infinitely generated H1, e.g. infinite graphs or fractals.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Advances in Mathematics | ||||
Publisher: | Academic Press | ||||
ISSN: | 0001-8708 | ||||
Official Date: | 2012 | ||||
Dates: |
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Volume: | Vol.229 | ||||
Number: | No.2 | ||||
Page Range: | pp. 935-967 | ||||
DOI: | 10.1016/j.aim.2011.10.015 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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