{"date_updated":"2026-07-08T06:48:58Z","title":"A non-Archimedean analogue of Teichmüller space and its tropicalization","status":"public","year":"2020","author":[{"full_name":"Ulirsch, Martin","first_name":"Martin","last_name":"Ulirsch","id":"114697"}],"user_id":"82981","_id":"66321","language":[{"iso":"eng"}],"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 $\\overline{\\mathcal{T}}_g$."}],"publication":"arXiv:2004.07508","citation":{"short":"M. Ulirsch, ArXiv:2004.07508 (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.","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} }","ama":"Ulirsch M. A non-Archimedean analogue of Teichmüller space and its tropicalization. <i>arXiv:200407508</i>. Published online 2020.","mla":"Ulirsch, Martin. “A Non-Archimedean Analogue of Teichmüller Space and Its Tropicalization.” <i>ArXiv:2004.07508</i>, 2020."},"type":"preprint","external_id":{"arxiv":["2004.07508"]},"date_created":"2026-07-08T06:48:52Z"}