[{"intvolume":"        27","date_updated":"2026-07-09T06:47:29Z","publication_status":"published","author":[{"full_name":"Ulirsch, Martin","last_name":"Ulirsch","first_name":"Martin","id":"114697"}],"publication_identifier":{"issn":["1022-1824","1420-9020"]},"title":"A non-Archimedean analogue of Teichmüller space and its tropicalization","year":"2021","doi":"10.1007/s00029-021-00651-4","language":[{"iso":"eng"}],"abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>In this article we use techniques from tropical and logarithmic geometry to construct a non-Archimedean analogue of<jats:italic>Teichmüller space</jats:italic><jats:inline-formula><jats:alternatives><jats:tex-math>$$\\overline{{{\\mathcal {T}}}}_g$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:msub><mml:mover><mml:mi>T</mml:mi><mml:mo>¯</mml:mo></mml:mover><mml:mi>g</mml:mi></mml:msub></mml:math></jats:alternatives></jats:inline-formula>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<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\overline{{\\mathcal {T}}}_g$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:msub><mml:mover><mml:mi>T</mml:mi><mml:mo>¯</mml:mo></mml:mover><mml:mi>g</mml:mi></mml:msub></mml:math></jats:alternatives></jats:inline-formula>.</jats:p>","lang":"eng"}],"issue":"3","publication":"Selecta Mathematica","type":"journal_article","date_created":"2026-07-08T06:48:52Z","status":"public","volume":27,"user_id":"82981","_id":"66321","publisher":"Springer Science and Business Media LLC","page":"39","citation":{"mla":"Ulirsch, Martin. “A Non-Archimedean Analogue of Teichmüller Space and Its Tropicalization.” <i>Selecta Mathematica</i>, vol. 27, no. 3, Springer Science and Business Media LLC, 2021, p. 39, doi:<a href=\"https://doi.org/10.1007/s00029-021-00651-4\">10.1007/s00029-021-00651-4</a>.","ama":"Ulirsch M. A non-Archimedean analogue of Teichmüller space and its tropicalization. <i>Selecta Mathematica</i>. 2021;27(3):39. doi:<a href=\"https://doi.org/10.1007/s00029-021-00651-4\">10.1007/s00029-021-00651-4</a>","bibtex":"@article{Ulirsch_2021, title={A non-Archimedean analogue of Teichmüller space and its tropicalization}, volume={27}, DOI={<a href=\"https://doi.org/10.1007/s00029-021-00651-4\">10.1007/s00029-021-00651-4</a>}, number={3}, journal={Selecta Mathematica}, publisher={Springer Science and Business Media LLC}, author={Ulirsch, Martin}, year={2021}, pages={39} }","apa":"Ulirsch, M. (2021). A non-Archimedean analogue of Teichmüller space and its tropicalization. <i>Selecta Mathematica</i>, <i>27</i>(3), 39. <a href=\"https://doi.org/10.1007/s00029-021-00651-4\">https://doi.org/10.1007/s00029-021-00651-4</a>","ieee":"M. Ulirsch, “A non-Archimedean analogue of Teichmüller space and its tropicalization,” <i>Selecta Mathematica</i>, vol. 27, no. 3, p. 39, 2021, doi: <a href=\"https://doi.org/10.1007/s00029-021-00651-4\">10.1007/s00029-021-00651-4</a>.","chicago":"Ulirsch, Martin. “A Non-Archimedean Analogue of Teichmüller Space and Its Tropicalization.” <i>Selecta Mathematica</i> 27, no. 3 (2021): 39. <a href=\"https://doi.org/10.1007/s00029-021-00651-4\">https://doi.org/10.1007/s00029-021-00651-4</a>.","short":"M. Ulirsch, Selecta Mathematica 27 (2021) 39."}}]