A collar lemma for partially hyperconvex surface group representations
We show that a collar lemma holds for Anosov representations of fundamental groups of surfaces into SL(n,R) that satisfy partial hyperconvexity properties inspired from Labourie’s work. This is the case for several open sets of Anosov representations not contained in higher rank Teichmüller space...
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| Hauptverfasser: | , |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
July 15, 2021
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| In: |
Transactions of the American Mathematical Society
Year: 2021, Jahrgang: 374, Heft: 10, Pages: 6927-6961 |
| ISSN: | 1088-6850 |
| DOI: | 10.1090/tran/8453 |
| Online-Zugang: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1090/tran/8453 Verlag, lizenzpflichtig, Volltext: https://www.ams.org/tran/2021-374-10/S0002-9947-2021-08453-6/ 
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| Verfasserangaben: | Jonas Beyrer and Beatrice Pozzetti |
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| 520 | |a We show that a collar lemma holds for Anosov representations of fundamental groups of surfaces into SL(n,R) that satisfy partial hyperconvexity properties inspired from Labourie’s work. This is the case for several open sets of Anosov representations not contained in higher rank Teichmüller spaces, as well as for Θ-positive representations into SO(p,q) if p≥4. We moreover show that ‘positivity properties’ known for Hitchin representations, such as being positively ratioed and having positive eigenvalue ratios, also hold for partially hyperconvex representations. | ||
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