Canonical Reducing Curves of Surface Homeomorphism

【摘要】 <正> In this paper we will introduce the concept of canonical reducing set of a surfacehomeomorphism,and prove that it is unique up to an isotopy.As an application,we will give a simple proof ofThurston’s theorem on classifying mappings on non-orientable surface,using the techniques of quasi-conformal mappings and some known results in the orientable case,especially the Thurston theorem onorientable surfaces.更多还原

【Abstract】 In this paper we will introduce the concept of canonical reducing set of a surface homeomorphism,and prove that it is unique up to an isotopy.As an application,we will give a simple proof of Thurston’s theorem on classifying mappings on non-orientable surface,using the techniques of quasi- conformal mappings and some known results in the orientable case,especially the Thurston theorem on orientable surfaces.更多还原