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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 S⁢L⁡(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: Beyrer, Jonas (VerfasserIn) , Pozzetti, Maria Beatrice (VerfasserIn)
Dokumenttyp: Article (Journal)
Sprache:Englisch
Veröffentlicht: July 15, 2021
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/
Volltext
Verfasserangaben:Jonas Beyrer and Beatrice Pozzetti
Beschreibung
Zusammenfassung:We show that a collar lemma holds for Anosov representations of fundamental groups of surfaces into S⁢L⁡(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 S⁢O⁡(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.
Beschreibung:Gesehen am 10.11.2021
Beschreibung:Online Resource
ISSN:1088-6850
DOI:10.1090/tran/8453

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