On the Classification of Surface Homeomorphisms
نویسنده
چکیده
The purpose of this article is to give a brief and elementary approach to the classification of mapping-classes for a surface with negative Euler characteristic. Work of Thurston ([9], [10], [7]) has brought out a deep analogy with the classical structure of the modular group SL2(Z) acting on the upper half plane H by constructing a completion of L, the space of simple loops in a base surface viewed modulo isotopy. This serves as the boundary sphere for a proper geometric action of the mapping-class group on Teichmüller space, a natural analogue of H. The theory has also been treated in this setting using techniques of extremal quasiconformal mappings by Bers [1]; for a detailed summary, which enlarges on the relationship between the present work and that cited above, the reader is referred to the article [3]. The book [Abikoff] presents an outline of the requisite Teichmüller theory as part of a selfcontained account to the approach of [Bers1].
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تاریخ انتشار 2002