Convexity of balls in outer space (Q2076056)
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scientific article; zbMATH DE number 7476302
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Convexity of balls in outer space |
scientific article; zbMATH DE number 7476302 |
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Convexity of balls in outer space (English)
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18 February 2022
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Summary: In this paper we study the convexity properties of geodesics and balls in Outer space equipped with the Lipschitz metric. We introduce a class of geodesics called balanced folding paths and show that, for every loop \(\alpha\), the length of \(\alpha\) along a balanced folding path is not larger than the maximum of its lengths at the endpoints. This implies that out-going balls are weakly convex. We then show that these results are sharp by providing several counter examples.
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outer space
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\(\mathrm{out}(\mathbb{F}_n)\)
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folding path
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