Cycle decompositions: From graphs to continua.
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 [Formula: see text]. This homology seems to be particularly apt for studying spaces with infinitely generated [Formula: see text], e.g. infinite graphs or fractals.
Technische Universität Graz, Steyrergasse 30, 8010 Graz, Austria.
Agelos
A
Georgakopoulos