Asymptoticity of grafting and Teichmüller rays
Asymptoticity of grafting and Teichmüller rays
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接枝和 Teichmüller 射线的渐近性
DOI：
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发表时间：
2011
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通讯作者：
Subhojoy Gupta
中科院分区：
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作者：
Subhojoy Gupta
本文证明了Teichmu ller空间中任意由非有理层或重曲线确定的嫁接射线都（强）渐近于Teichmu ller测地线.因此，一般嫁接射线到模空间的投影是稠密的。我们还证明了在Teichmu ller空间中对任意双曲曲面进行整数（2 π-）嫁接所得到的点集投影到一个稠密集上，这意味着具有任意固定Fuchsian完整性的复射影曲面在模空间中是稠密的.
We show that any grafting ray in Teichm"{u}ller space determined by an arational lamination or a multi-curve is (strongly) asymptotic to a Teichm"{u}ller geodesic ray. As a consequence the projection of a generic grafting ray to moduli space is dense. We also show that the set of points in Teichm"{u}ller space obtained by integer (2pi-) graftings on any hyperbolic surface projects to a dense set, which implies that complex projective surfaces with any fixed Fuchsian holonomy are dense in moduli space.