Basmajian's identity over non-Archimedean local fields

Yan Mary He; Chenxi Wu

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arXiv · 2212.09992

Basmajian's identity over non-Archimedean local fields

Yan Mary He·Chenxi Wu

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Abstract

Let $Σ$ be a connected compact oriented surface with boundary and negative Euler characteristic. Let $k$ be a non-Archimedean local field. In this paper, we prove Basmajian's identity for projective Anosov representations $ρ\colon π_1Σ\to {\rm PSL}(d,k), d\ge 2$. Our series identity exhibits a drastic difference from all the Basmajian-type identities over the Archimedean fields $\mathbb{R}$ and $\mathbb{C}$. In particular, the series is a signed finite sum. When $d=2$, we give a geometric proof of the identity using Berkovich hyperbolic geometry.

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BibTeX RIS

Yan Mary He, Chenxi Wu. 2024-11-25. Basmajian's identity over non-Archimedean local fields. https://arxiv.org/abs/2212.09992

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