Global structure of continuous flows on 2-manifolds
Global structure of continuous flows on 2-manifolds
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2 流形上连续流的全局结构
DOI：
10.1016/0022-0396(76)90006-1
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发表时间：
1976
影响因子：
2.4
通讯作者：
Thomas O’Brien
中科院分区：
文献类型：
--
作者：
D. A. Neumann;Thomas O’Brien
在本文中，我们考虑任意2-流形（可分度量，但不一定是紧的，也不一定是可定向的，可能有边界）上的连续流。两个这样的流（M，4）和（M '，$'）是（拓扑）等价的，如果存在M到M '的同胚，它将4的轨道带到+'保持意义的轨道上（但不一定参数化）。商空间M/4，通过将（M，4）的轨道坍缩为点而得到，给出了一个简单的结构，导致流的轨道复形K（4）。然后我们得到以下结果：
In this paper we consider continuous flows on arbitrary 2-manifolds (separable metric, but not necessarily compact nor orientable and possibly with boundary). Two such flows,(M, 4) and (M’, $‘), are (topologically) equivalent if there is a homeomorphism of M onto M’which takes orbits of 4 onto orbits of+’preserving sense (but not necessarily parametrization). The quotient space M/4, obtained by collapsing orbits of (M, 4) to points, is given a simple structure resulting in the orbit complex K (4) of the flow. We then have the following results: