Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 45, 2020, 673–685

TOTALLY GEODESIC HOMEOMORPHISMS BETWEEN TEICHMÜLLER SPACES

Dong Tan

Guangxi University, College of Mathematics and Information Science
530000, Guangxi, P.R. China; duzuizhe2013 'at' foxmail.com

Abstract. First, we show that a projective measured foliation is a Busemann point, in Gardiner–Masur boundary, if and only if it is indecomposable. Let f : T_g,n → T_g,n be a totally geodesic homeomorphism and suppose that f admits a homeomorphic extension to ∂_GMT_g,n. We show that f induces a simplicial automorphism of curve complex. Moreover, the restriction of f on T_g,n is an isometry. As an application, we obtain an alternative proof of Royden's Theorem.

2010 Mathematics Subject Classification: Primary 32G15, 30F60, 57M50.

Key words: Gardiner–Masur boundary, mapping class group, Teichmüller space, totally geodesic.

Reference to this article: D. Tan: Totally geodesic homeomorphisms between Teichmüller spaces. Ann. Acad. Sci. Fenn. Math. 45 (2020), 673–685.

Full document as PDF file

https://doi.org/10.5186/aasfm.2020.4538