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Non-Hitchin Borel Anosov representations from surface groups to SL3kℝ
Abstract
We use the Labourie--Wentworth's formula and the thermodynamic formalism to show that, along the slice constructed by Bronstein--Davalo, the logarithmic top-eigenvalue length spectrum has a uniformly positive second variation near the Barbot representation. As a major application, we show that every closed surface group admits a non-Hitchin Borel Anosov representation into SL3kℝ for every kgeqslant 1. In particular, we obtain the first such examples in the even dimensions 6k. We also study the local behavior of related objects of this slice around the Barbot representation, including the Lyapunov exponent of the flat bundle, the Hausdorff dimension of the limit set, and the Hilbert entropy of the representation.
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BibTeX
@misc{yao2026nonhitchin,
title = {{Non-Hitchin Borel Anosov representations from surface groups to $\mathrmSL_3k\mathbbR$}},
author = {Zhufeng Yao and Junming Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12809},
eprint = {2609.12809},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12809},
}
RIS
TY - UNPB
TI - Non-Hitchin Borel Anosov representations from surface groups to SL_3kℝ
AU - Zhufeng Yao
AU - Junming Zhang
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.12809
UR - https://arxiv.org/abs/2609.12809
AB - We use the Labourie--Wentworth's formula and the thermodynamic formalism to show that, along the slice constructed by Bronstein--Davalo, the logarithmic top-eigenvalue length spectrum has a uniformly positive second variation near the Barbot representation. As a major application, we show that every closed surface group admits a non-Hitchin Borel Anosov representation into SL_3kℝ for every kgeqslant 1. In particular, we obtain the first such examples in the even dimensions 6k. We also study the local behavior of related objects of this slice around the Barbot representation, including the Lyapunov exponent of the flat bundle, the Hausdorff dimension of the limit set, and the Hilbert entropy of the representation.
ER -