Complete semi-conjugacies for psuedo-Anosov homeomorphisms
نویسندگان
چکیده
Suppose S is a surface of genus ≥ 2, f : S → S is a surface homeomorphism isotopic to a pseudo-Anosov map α and suppose S̃ is the universal cover of S and F and A are lifts of f and α respectively. A result of A. Fathi shows there is a semiconjugacy Θ : S̃ → L̄ × L̄ from F to Ā, where L̄ (L̄) is the completion of the R-tree of leaves of the stable (resp. unstable) foliation for A and Ā is the map induced by A. We generalize a result of Markovich and show that for any g ∈ Homeo(S) that commutes with f and is isotopic to the identity with identity lift G and for any (c, w) in the image of Θ each component of Θ−1(c, w) is G-invariant.
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