منابع مشابه
Skinning Maps Are Finite-to-one
Skinning maps were introduced by William Thurston in the proof of the Geometrization Theorem for Haken 3-manifolds (see [Ota]). At a key step in the proof one has a compact 3-manifold M with nonempty boundary whose interior admits a hyperbolic structure. The interplay between deformations of the hyperbolic structure and the topology of M and ∂M determines a holomorphic map of Teichmüller spaces...
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Let f : X → Y be a σ-perfect k-dimensional surjective map of metrizable spaces such that dimY ≤ m. It is shown that, for every integer p ≥ 1 there exists a dense Gδ-subset H(k,m, p) of C(X, I k+p ) with the source limitation topology such that each fiber of f△g, g ∈ H(k,m, p), contains at most max{k+m−p+2, 1} points. This result provides a proof of Hypothesis 1 and Hypothesis 2 from [1].
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To Ken Kunen on the occasion of his retirement from teaching MSC: primary 54F45 secondary 54C10, 54G05
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Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This paper has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library In this paper we def...
متن کاملGeometry of Geometrically Finite One-Dimensional Maps
We study the geometry of certain one-dimensional maps as dynamical systems. We prove the property of bounded and bounded nearby geometry of certain C one-dimensional maps with finitely many critical points. This property enables us to give the quasίsymmetric classification of geometrically finite one-dimensional maps.
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ژورنال
عنوان ژورنال: Acta Mathematica
سال: 2015
ISSN: 0001-5962
DOI: 10.1007/s11511-015-0129-6