Positivity, cross-ratios and the Collar Lemma
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916387867328512 |
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| author | Beyrer, Jonas Guichard, Olivier Labourie, François Pozzetti, Beatrice Wienhard, Anna |
| author_facet | Beyrer, Jonas Guichard, Olivier Labourie, François Pozzetti, Beatrice Wienhard, Anna |
| contents | We prove that $Θ$-positive representations of fundamental groups of surfaces (possibly cusped or of infinite type) satisfy a collar lemma, and their associated cross-ratios are positive. As a consequence we deduce that $Θ$-positive representations form closed subsets of the representation variety. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_06294 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Positivity, cross-ratios and the Collar Lemma Beyrer, Jonas Guichard, Olivier Labourie, François Pozzetti, Beatrice Wienhard, Anna Differential Geometry Group Theory We prove that $Θ$-positive representations of fundamental groups of surfaces (possibly cusped or of infinite type) satisfy a collar lemma, and their associated cross-ratios are positive. As a consequence we deduce that $Θ$-positive representations form closed subsets of the representation variety. |
| title | Positivity, cross-ratios and the Collar Lemma |
| topic | Differential Geometry Group Theory |
| url | https://arxiv.org/abs/2409.06294 |