A collar lemma for partially hyperconvex surface group representations
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- by Jonas Beyrer and Beatrice Pozzetti PDF
- Trans. Amer. Math. Soc. 374 (2021), 6927-6961 Request permission
Abstract:
We show that a collar lemma holds for Anosov representations of fundamental groups of surfaces into $SL(n,\mathbb {R})$ 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 $\Theta$-positive representations into $SO(p,q)$ if $p\geq 4$. 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.References
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Additional Information
- Jonas Beyrer
- Affiliation: I.H.E.S., 35 Route de Chartres, 91440 Bures-sur-Yvette, France
- MR Author ID: 1239913
- ORCID: 0000-0003-2636-6943
- Beatrice Pozzetti
- Affiliation: Heidelberg University, Im Neuenheimer feld 205, 69120 Heidelberg, Germany
- MR Author ID: 1060633
- ORCID: 0000-0002-9238-1087
- Received by editor(s): April 15, 2020
- Received by editor(s) in revised form: May 5, 2020, and December 19, 2020
- Published electronically: July 15, 2021
- Additional Notes: The first author acknowledges funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), 338644254 (SPP2026), and the Schweizerischer Nationalfonds (SNF, Swiss Research Foundation), P2ZHP2 184022 (Early Postdoc.Mobility). The second author acknowledges funding by the DFG, 427903332 (Emmy Noether). Both authors acknowledge funding by the DFG, 281869850 (RTG 2229)
- © Copyright 2021 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 374 (2021), 6927-6961
- MSC (2020): Primary 22E40, 57M50
- DOI: https://doi.org/10.1090/tran/8453
- MathSciNet review: 4315593