Graphs of curves on infinite-type surfaces with mapping class group actions
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....
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| Main Authors: | , |
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| Format: | Article (Journal) Chapter/Article |
| Language: | English |
| Published: |
2 Nov 2016
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| In: |
Arxiv
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| Online Access: | Verlag, kostenfrei, Volltext: http://arxiv.org/abs/1611.00841
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| Author Notes: | Matthew Gentry Durham, Federica Fanoni, and Nicholas G. Vlamis |
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| 520 | |a 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. | ||
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