A quasiconformal mapping class group acting trivially on the asymptotic Teichmüller space
HTML articles powered by AMS MathViewer
- by Katsuhiko Matsuzaki PDF
- Proc. Amer. Math. Soc. 135 (2007), 2573-2579 Request permission
Abstract:
For an analytically infinite Riemann surface $R$, the quasiconformal mapping class group $\operatorname {MCG}(R)$ always acts faithfully on the ordinary Teichmüller space $T(R)$. However in this paper, an example of $R$ is constructed for which $\operatorname {MCG}(R)$ acts trivially on its asymptotic Teichmüller space $AT(R)$.References
- Clifford J. Earle and Frederick P. Gardiner, Geometric isomorphisms between infinite-dimensional Teichmüller spaces, Trans. Amer. Math. Soc. 348 (1996), no. 3, 1163–1190. MR 1322950, DOI 10.1090/S0002-9947-96-01490-0
- C. Earle, F. Gardiner and N. Lakic, Teichmüller spaces with asymptotic conformal equivalence, I.H.E.S. Preprint (1995).
- C. J. Earle, F. P. Gardiner, and N. Lakic, Asymptotic Teichmüller space. I. The complex structure, In the tradition of Ahlfors and Bers (Stony Brook, NY, 1998) Contemp. Math., vol. 256, Amer. Math. Soc., Providence, RI, 2000, pp. 17–38. MR 1759668, DOI 10.1090/conm/256/03995
- Clifford J. Earle, Frederick P. Gardiner, and Nikola Lakic, Asymptotic Teichmüller space. II. The metric structure, In the tradition of Ahlfors and Bers, III, Contemp. Math., vol. 355, Amer. Math. Soc., Providence, RI, 2004, pp. 187–219. MR 2145063, DOI 10.1090/conm/355/06452
- Clifford J. Earle, Vladimir Markovic, and Dragomir Saric, Barycentric extension and the Bers embedding for asymptotic Teichmüller space, Complex manifolds and hyperbolic geometry (Guanajuato, 2001) Contemp. Math., vol. 311, Amer. Math. Soc., Providence, RI, 2002, pp. 87–105. MR 1940165, DOI 10.1090/conm/311/05448
- Ege Fujikawa, The action of geometric automorphisms of asymptotic Teichmüller spaces, Michigan Math. J. 54 (2006), no. 2, 269–282. MR 2252759, DOI 10.1307/mmj/1156345593
- Frederick P. Gardiner and Dennis P. Sullivan, Symmetric structures on a closed curve, Amer. J. Math. 114 (1992), no. 4, 683–736. MR 1175689, DOI 10.2307/2374795
- Vladimir Markovic, Biholomorphic maps between Teichmüller spaces, Duke Math. J. 120 (2003), no. 2, 405–431. MR 2019982, DOI 10.1215/S0012-7094-03-12028-1
- Katsuhiko Matsuzaki, A countable Teichmüller modular group, Trans. Amer. Math. Soc. 357 (2005), no. 8, 3119–3131. MR 2135738, DOI 10.1090/S0002-9947-04-03765-1
- K. Matsuzaki, Quasiconformal mapping class groups having common fixed points on the asymptotic Teichmüller spaces, J. Analyse Math., to appear.
Additional Information
- Katsuhiko Matsuzaki
- Affiliation: Department of Mathematics, Ochanomizu University, Tokyo 112-8610, Japan
- Address at time of publication: Department of Mathematics, Okayama University, Okayama 700-8530, Japan
- MR Author ID: 294335
- ORCID: 0000-0003-0025-5372
- Email: matsuzak@math.okayama-u.ac.jp
- Received by editor(s): August 16, 2005
- Received by editor(s) in revised form: April 19, 2006
- Published electronically: March 22, 2007
- Communicated by: Juha M. Heinonen
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 2573-2579
- MSC (2000): Primary 30F60; Secondary 32G15
- DOI: https://doi.org/10.1090/S0002-9939-07-08761-8
- MathSciNet review: 2302578