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Cycle decompositions: From graphs to continua
- Source :
-
Advances in Mathematics . Jan2012, Vol. 229 Issue 2, p935-967. 33p. - Publication Year :
- 2012
-
Abstract
- 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 . This homology seems to be particularly apt for studying spaces with infinitely generated , e.g. infinite graphs or fractals. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 00018708
- Volume :
- 229
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Advances in Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 67512852
- Full Text :
- https://doi.org/10.1016/j.aim.2011.10.015