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Canonical reducing curves of surface homeomorphism. (English) Zbl 0651.57008

We introduce the concept of canonical reducing set of a surface homeomorpism, and prove that it is unique up to an isotopy. As an applicaton, we give a simpler 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.

MSC:

57N05 Topology of the Euclidean \(2\)-space, \(2\)-manifolds (MSC2010)
57R50 Differential topological aspects of diffeomorphisms
37D99 Dynamical systems with hyperbolic behavior
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References:

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