Abstract
The arc metric is an asymmetric metric on the Teichmüller space T(S) of a surface S with nonempty boundary. It is the analogue of Thurston's metric on the Teichmüller space of a surface without boundary. In this paper we study the relation between Thurston's compactification and the horofunction compactification of T(S) endowed with the arc metric. We prove that there is a natural homeomorphism between the two compactifications. This generalizes a result of Walsh [20] that concerns Thurston's metric.
| Original language | English |
|---|---|
| Pages (from-to) | 160-191 |
| Number of pages | 32 |
| Journal | Topology and its Applications |
| Volume | 208 |
| DOIs | |
| State | Published - 1 Aug 2016 |
Keywords
- Arc metric
- Horofunction
- Thurston's asymmetric metric
- Thurston's compactification
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