标题： 有序阿贝尔群在CW复形上 显示英文标题

标题： Ordered abelian groups over a CW complex

摘要： 如果X是一个CW复形，可以为X的每个点分配一个有限秩的有序阿贝尔群，其正元素子集连续地依赖于X的点。 这种以这种方式出现的局部平凡丛我们记为 E(X). 在本工作中，我们根据X的系数在环Z_2上的第一上同调群对这类丛进行了拓扑分类。 这个结果在紧致流形上的叶状结构特征类理论中有一个令人惊讶的应用。 显示英文摘要

摘要： If X is a CW complex, one can assign to each point of X an ordered abelian group of finite rank whose subset of positive elements depends continuously on the points of X. A locally trivial bundle which arises in this way we denote by E(X). In the present work we establish a topological classification of such bundles in terms of the first cohomology group of X with coefficients in the ring Z_2. This result has an amazing application in the theory of characteristic classes of foliations on compact manifolds.