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Showing 1 to 5 of 5 for “"Curve complex"”.
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The Asymptotic Cone of Teichmuller Space: Thickness and Divergence
Using the geometric model of the pants complex, we study the Asymptotic Cone of Teichmüller space equipped with the Weil Petersson metric. In particular, we provide a characterization of the canonical finest pieces in the tree-graded structure of the asymptotic cone of Teichmüller space along the …
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Combinatorial models for surface and free group symmetries
The curve complex of Harvey allows combinatorial representation of a surface mapping class group by describing its action on simple closed curves. Similar complexes of spheres, free factors, and free splittings allow combinatorial representation of the automorphisms of a free group. We consider a …
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The geometry of end-periodic mapping tori
… whose leaves naturally project to the arc and curve complex of a given compact subsurface $Y\subset S$. As an end-periodic analogy to work of Minsky in the finite-type setting, we show that for every $\epsilon>0$ there exists $K> 0$ (depending only on $\epsilon$ and the \emph{capacity} of $f$) …
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Subgroups of the Torelli group
… by Dehn twists about symmetric separating curves denoted H(Sg). We will show the well-known Birman-Craggs-Johnson homomorphism is not able to distinguish among SI(Sg), H(Sg), or K(Sg), where K(Sg) is the subgroup generated by Dehn twists about separating curves. Elements of H(Sg) act …
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Gromov boundaries of complexes associated to surfaces
In 1996, Masur and Minsky showed that the curve graph is hyperbolic. Recently, Hensel, Przytycki, and Webb proved a stronger result which was the uniform hyperbolicity of the curve graph, and they also gave the first proof of the uniform hyperbolicity of the arc graph using unicorn arcs. For closed …