Circle homeomorphisms and shears
英文摘要:
We give parameterizations of homeomorphisms, quasisymmetric maps and symmetric maps of the unit circle in terms of shear coordinates for the Farey tesselation.
机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。
Dragomir Saric
We give parameterizations of homeomorphisms, quasisymmetric maps and symmetric maps of the unit circle in terms of shear coordinates for the Farey tesselation.
机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。
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Circle homeomorphisms with square summable diamond shears
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Pivoting technique for the circle homeomorphism group
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In the first part of the paper we describe the complex geometry of the universal Teichmüller space $\mathcal T$, which may be realized as an open subset in the complex Banach space of holomorphic quadratic differentials in the unit disc. The quotient $\mathcal S$ of the diffeomorphism group of the circle modulo Möbius transformations may be treated as a smooth part of $\mathcal T$. In the second part we consider the quantization of universal Teichmüller space $\mathcal T$. We explain first how to quantize the smooth part $\mathcal S$ by embedding it into a Hilbert-Schmidt Siegel disc. This qua…
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Random actions of homeomorphisms of Cantor sets embedded in a line and Tits alternative
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We give an elementary proof of a theorem that characterizes quasisymmetric maps of the unit circle in terms of shear coordinates on the Farey tesselation. The proof only uses the normal family argument for quasisymmetric maps and some elementary hyperbolic geometry.
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该研究通过单位圆盘法里镶嵌上拟对称同胚诱导的剪切函数等价类,给出开单位圆盘渐近Teichmuller空间的参数化,定义三种新度量并证明其拓扑与Teichmuller度量拓扑等价,同时纠正了相关文献的一处证明错误。
Suppose that f and g are Markov surjections, each defined on a wedge of circles, each fixing the branch point and having the branch point as the only critical value. We show that if the points in the inverse limit spaces associated with f and g corresponding to the branch point are distinguished then these inverse limit spaces are homeomorphic if and only if the substitutions associated with f and g are weakly equivalent. This, and related results, are applied to one-dimensional substitution tiling spaces, one-dimensional unstable manifolds of hyperbolic sets, and inverse limits of tent maps w…
We give a new lower bound on the number of connected components of the space of representations of a surface group into the group of orientation preserving homeomorphisms of the circle. Precisely, for the fundamental group of a genus g surface, we show there are at least k^(2g) + 1 connected components containing representations with Euler number (2g-2)/(k). We also show that certain representations are rigid, meaning that all deformations lie in the same semiconjugacy class. Our methods apply to representations of surface groups into finite covers of PSL(2,R) and into Diff+(S^1) as well, in w…
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