Year: 2022
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: He, Yan Mary, Wu, Chenxi
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4312090727