论文标题
Basmajian对非架构的本地领域的身份
Basmajian's identity over non-Archimedean local fields
论文作者
论文摘要
令$σ$为具有边界和负欧特征的连接的紧凑型表面。令$ k $为非架构的本地领域。在本文中，我们证明了Basmajian在投射Anosov表示的身份$ρ\colonπ_1σ\ to {\ rm psl}（d，k），d \ ge 2 $。我们的系列身份与Archimedean Fields $ \ Mathbb {r} $和$ \ Mathbb {C} $上的所有Basmajian类型身份表现出巨大的差异。特别是，该系列是签名有限的总和。当$ d = 2 $时，我们使用Berkovich双曲几何形状给出了身份的几何证明。
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.
