We study the geometry of horospheres in Teichmüller space of Riemann surfaces of genus with punctures, where . We show that every -diffeomorphism of Teichmüller space to itself that preserves horospheres is an element of the extended mapping class group. Using the relation between horospheres and metric balls, we obtain a new proof of Royden’s Theorem that the isometry group of the Teichmüller metric is the extended mapping class group.
Nous étudions la géométrie des horosphéres dans l’espace de Teichmüller des surfaces de Riemann de genre avec perforations, oú . Nous montrons que chaque -difféomorphisme de l’espace de Teichmüller dans lui-même qui préserve les horosphéres est un élément du groupe mapping class étendu. En utilisant la relation entre les horosphéres et les boules métriques, nous obtenons une nouvelle preuve du théoréme de Royden qui affirme que le groupe d’isométrie de la métrique de Teichmüller est le groupe mapping class étendu.
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Keywords: Extremal length, horosphere, mapping class group, Teichmüller space.
Mot clés : longueur extrémale, horosphère, groupe mapping class, espace de Teichmüller
Su, Weixu 1; Tan, Dong 2
@article{AIF_2023__73_4_1677_0, author = {Su, Weixu and Tan, Dong}, title = {Horospheres in {Teichm\"uller} space and mapping class group}, journal = {Annales de l'Institut Fourier}, pages = {1677--1707}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {73}, number = {4}, year = {2023}, doi = {10.5802/aif.3556}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3556/} }
TY - JOUR AU - Su, Weixu AU - Tan, Dong TI - Horospheres in Teichmüller space and mapping class group JO - Annales de l'Institut Fourier PY - 2023 SP - 1677 EP - 1707 VL - 73 IS - 4 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3556/ DO - 10.5802/aif.3556 LA - en ID - AIF_2023__73_4_1677_0 ER -
%0 Journal Article %A Su, Weixu %A Tan, Dong %T Horospheres in Teichmüller space and mapping class group %J Annales de l'Institut Fourier %D 2023 %P 1677-1707 %V 73 %N 4 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3556/ %R 10.5802/aif.3556 %G en %F AIF_2023__73_4_1677_0
Su, Weixu; Tan, Dong. Horospheres in Teichmüller space and mapping class group. Annales de l'Institut Fourier, Volume 73 (2023) no. 4, pp. 1677-1707. doi : 10.5802/aif.3556. https://aif.centre-mersenne.org/articles/10.5802/aif.3556/
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