説明
<p>Under a certain geometric assumption on a hyperbolic Riemann surface, we prove an asymptotic version of the fixed point theorem for the Teichmüller modular group, which asserts that every finite subgroup of the asymptotic Teichmüller modular group has a common fixed point in the asymptotic Teichmüller space. For its proof, we use a topological characterization of the asymptotically trivial mapping class group, which has been obtained in the authors’ previous paper, but a simpler argument is given here. As a consequence, every finite subgroup of the asymptotic Teichmüller modular group is realized as a group of quasiconformal automorphisms modulo coincidence near infinity. Furthermore, every finite subgroup of a certain geometric automorphism group of the asymptotic Teichmüller space is realized as an automorphism group of the Royden boundary of the Riemann surface. These results can be regarded as asymptotic versions of the Nielsen realization theorem.</p>
収録刊行物
-
- Transactions of the American Mathematical Society
-
Transactions of the American Mathematical Society 365 (6), 3309-3327, 2013-01-04
American Mathematical Society (AMS)
- Tweet
詳細情報 詳細情報について
-
- CRID
- 1360848659423069696
-
- ISSN
- 10886850
- 00029947
-
- データソース種別
-
- Crossref
- KAKEN