将旋转区间推广到图的顶点映射
Generalizing the rotation interval to vertex maps on graphs
摘要：
研究了与恒等式同伦且顶点置换的图映射。给定这样一个映射的一个周期点，用基本群定义一个{ \em旋转元}。证明了图的给定边中与周期点有关的旋转元的若干结果。大多数结果表明，存在两个具有某些转动元素的周期点将意味着存在一个无限族的其他具有相关转动元素的周期点。这些关于周期点的结果可以看作是圆的一次映射的旋转区间的推广。
英文摘要：
Graph maps that are homotopic to the identity and that permute the vertices are studied. Given a periodic point for such a map, a {\em rotation element} is defined in terms of the fundamental group. A number of results are proved about the rotation elements associated to periodic points in a given edge of the graph. Most of the results show that the existence of two periodic points with certain rotation elements will imply an infinite family of other periodic points with related rotation elements. These results for periodic points can be considered as generalizations of the rotation interval for degree one maps of the circle.
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