preprint Martin Ulirsch author 114697 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 $\overline{\mathcal{T}}_g$. 2020 eng 2004.07508 @article{Ulirsch_2020, title={A non-Archimedean analogue of Teichmüller space and its tropicalization}, journal={arXiv:2004.07508}, author={Ulirsch, Martin}, year={2020} } Ulirsch M. A non-Archimedean analogue of Teichmüller space and its tropicalization. <i>arXiv:200407508</i>. Published online 2020. Ulirsch, Martin. “A Non-Archimedean Analogue of Teichmüller Space and Its Tropicalization.” <i>ArXiv:2004.07508</i>, 2020. M. Ulirsch, ArXiv:2004.07508 (2020). Ulirsch, Martin. “A Non-Archimedean Analogue of Teichmüller Space and Its Tropicalization.” <i>ArXiv:2004.07508</i>, 2020. M. Ulirsch, “A non-Archimedean analogue of Teichmüller space and its tropicalization,” <i>arXiv:2004.07508</i>. 2020. Ulirsch, M. (2020). A non-Archimedean analogue of Teichmüller space and its tropicalization. In <i>arXiv:2004.07508</i>. 663212026-07-08T06:48:52Z2026-07-08T06:48:58Z