{"abstract":[{"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 $\\overline{\\mathcal{T}}_g$.","lang":"eng"}],"citation":{"apa":"Ulirsch, M. (2020). A non-Archimedean analogue of Teichmüller space and its tropicalization. In <i>arXiv:2004.07508</i>.","ieee":"M. Ulirsch, “A non-Archimedean analogue of Teichmüller space and its tropicalization,” <i>arXiv:2004.07508</i>. 2020.","chicago":"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).","mla":"Ulirsch, Martin. “A Non-Archimedean Analogue of Teichmüller Space and Its Tropicalization.” <i>ArXiv:2004.07508</i>, 2020.","ama":"Ulirsch M. A non-Archimedean analogue of Teichmüller space and its tropicalization. <i>arXiv:200407508</i>. Published online 2020.","bibtex":"@article{Ulirsch_2020, title={A non-Archimedean analogue of Teichmüller space and its tropicalization}, journal={arXiv:2004.07508}, author={Ulirsch, Martin}, year={2020} }"},"publication":"arXiv:2004.07508","type":"preprint","date_created":"2026-07-08T06:47:06Z","external_id":{"arxiv":["2004.07508"]},"date_updated":"2026-07-08T06:47:11Z","author":[{"full_name":"Ulirsch, Martin","last_name":"Ulirsch","first_name":"Martin"}],"title":"A non-Archimedean analogue of Teichmüller space and its tropicalization","year":"2020","status":"public","user_id":"82981","language":[{"iso":"eng"}],"_id":"66320"}