Georgakopoulos Agelos
Technische Universität Graz, Steyrergasse 30, 8010 Graz, Austria.
Adv Math (N Y). 2012 Jan 30;229(2):935-967. doi: 10.1016/j.aim.2011.10.015.
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.
我们将一个基本的图论事实推广到任意连续统，该事实表明图的圈空间的每个元素都是边不相交圈的和。为实现这一点，我们用拓扑圆代替图圈，并用连续统的一个新的同调群代替图的圈空间，这个同调群是第一奇异同调群[公式：见正文]的商。这个同调似乎特别适合研究具有无限生成的[公式：见正文]的空间，例如无限图或分形。
