A closed ball compactification of a maximal component via cores of trees
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866912342018621440 |
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| author | Martone, Giuseppe Ouyang, Charles Tamburelli, Andrea |
| author_facet | Martone, Giuseppe Ouyang, Charles Tamburelli, Andrea |
| contents | We show that, in the character variety of surface group representations into the Lie group $\mathrm{PSL}(2,\mathbb{R}) \times \mathrm{PSL}(2,\mathbb{R})$, the compactification of the maximal component introduced by the second author is a closed ball upon which the mapping class group acts. We study the dynamics of this action. Finally, we describe the boundary points geometrically as $(\overline{A_{1} \times A_{1}},2)$-valued mixed structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_06106 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A closed ball compactification of a maximal component via cores of trees Martone, Giuseppe Ouyang, Charles Tamburelli, Andrea Geometric Topology Metric Geometry We show that, in the character variety of surface group representations into the Lie group $\mathrm{PSL}(2,\mathbb{R}) \times \mathrm{PSL}(2,\mathbb{R})$, the compactification of the maximal component introduced by the second author is a closed ball upon which the mapping class group acts. We study the dynamics of this action. Finally, we describe the boundary points geometrically as $(\overline{A_{1} \times A_{1}},2)$-valued mixed structures. |
| title | A closed ball compactification of a maximal component via cores of trees |
| topic | Geometric Topology Metric Geometry |
| url | https://arxiv.org/abs/2110.06106 |