Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 32, 2007, 55-71
Tokyo Denki University, Department of Mathematical Sciences
Ishizaka, Hatoyama, Hiki, Saitama, 350-0394, Japan;
miyachi 'at' r.dendai.ac.jp
Abstract. In this paper, we will introduce a new kind of isomorphism theorem (we call it the reducing theorem) for asymptotic Teichmüller spaces. Our isomorphism theorem is induced by (conformal) 2-surgery operations along simple closed loops on surfaces, and yields several interesting and pathological phenomena on the structures of asymptotic Teichmüller spaces.
2000 Mathematics Subject Classification: Primary 32G15, 30F25, 30F60.
Key words: Teichmüller space, asymptotic Teichmüller space, Teichmüller theory, quasiconformal isotopy.
Reference to this article: H. Miyachi: A reduction for asymptotic Teichmüller spaces. Ann. Acad. Sci. Fenn. Math. 32 (2007), 55-71.
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