---
_id: '66321'
abstract:
- lang: eng
  text: In this article we use techniques from tropical and logarithmic geometry to
    construct a non-Archimedean analogue of Teichmüller space $\overline{\mathcal{T}}_g$
    whose points are pairs consisting of a stable projective curve over a non-Archimedean
    field and a Teichmüller marking of the topological fundamental group of its Berkovich
    analytification. This construction is closely related to and inspired by the classical
    construction of a non-Archimedean Schottky space for Mumford curves by Gerritzen
    and Herrlich. We argue that the skeleton of non-Archimedean Teichmüller space
    is precisely the tropical Teichmüller space introduced by Chan-Melo-Viviani as
    a simplicial completion of Culler-Vogtmann Outer space. As a consequence, Outer
    space turns out to be a strong deformation retract of the locus of smooth Mumford
    curves in $\overline{\mathcal{T}}_g$.
author:
- first_name: Martin
  full_name: Ulirsch, Martin
  id: '114697'
  last_name: Ulirsch
citation:
  ama: Ulirsch M. A non-Archimedean analogue of Teichmüller space and its tropicalization.
    <i>arXiv:200407508</i>. Published online 2020.
  apa: Ulirsch, M. (2020). A non-Archimedean analogue of Teichmüller space and its
    tropicalization. In <i>arXiv:2004.07508</i>.
  bibtex: '@article{Ulirsch_2020, title={A non-Archimedean analogue of Teichmüller
    space and its tropicalization}, journal={arXiv:2004.07508}, author={Ulirsch, Martin},
    year={2020} }'
  chicago: Ulirsch, Martin. “A Non-Archimedean Analogue of Teichmüller Space and Its
    Tropicalization.” <i>ArXiv:2004.07508</i>, 2020.
  ieee: M. Ulirsch, “A non-Archimedean analogue of Teichmüller space and its tropicalization,”
    <i>arXiv:2004.07508</i>. 2020.
  mla: Ulirsch, Martin. “A Non-Archimedean Analogue of Teichmüller Space and Its Tropicalization.”
    <i>ArXiv:2004.07508</i>, 2020.
  short: M. Ulirsch, ArXiv:2004.07508 (2020).
date_created: 2026-07-08T06:48:52Z
date_updated: 2026-07-08T06:48:58Z
external_id:
  arxiv:
  - '2004.07508'
language:
- iso: eng
publication: arXiv:2004.07508
status: public
title: A non-Archimedean analogue of Teichmüller space and its tropicalization
type: preprint
user_id: '82981'
year: '2020'
...