Graphs of curves on infinite-type surfaces with mapping class group actions
Graphs of curves on infinite-type surfaces with mapping class group actions
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具有映射类组动作的无限型曲面上的曲线图
DOI：
10.5802/aif.3217
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
N. Vlamis
中科院分区：
文献类型：
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作者：
Matthew Gentry Durham;Federica Fanoni;N. Vlamis
研究了无限型曲面$S$的映射类群在$S$上的顶点为简单闭曲线的连通图上是否允许具有无界轨道的作用。我们为无穷型曲面引入了一个拓扑不变量，它决定了在许多情况下是否存在这样的作用。这使我们可以得出结论，作为非局部紧拓扑群，许多大映射类群具有Rosendal意义上的非平凡粗糙几何。
We study when the mapping class group of an infinite-type surface $S$ admits an action with unbounded orbits on a connected graph whose vertices are simple closed curves on $S$. We introduce a topological invariant for infinite-type surfaces that determines in many cases whether there is such an action. This allows us to conclude that, as non-locally compact topological groups, many big mapping class groups have nontrivial coarse geometry in the sense of Rosendal.