Hyperbolicity of the genus two Hatcher–Thurston complex
Hyperbolicity of the genus two Hatcher–Thurston complex
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DOI：
10.1007/s00209-012-1009-9
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发表时间：
2013-02
影响因子：
0.8
通讯作者：
Youlin Li;Jiming Ma
中科院分区：
文献类型：
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作者：
Youlin Li;Jiming Ma
对于带标点符号f1，n的1属曲面，我们证明了Hatcher-Thurston复合体$${\fancyscript{HT}(F_{1,n})}$$是双曲的。对于2属封闭曲面ef2，我们证明了Hatcher-Thurston复合体$${\fancyscript{HT}(F_{2})}$$相对于它的子空间Xγ族是强相对双曲的，其中γ的范围在所有分离曲线ofF2上，并且每个Xγ与两个Farey图的积是等距的。{}
For the genus 1 surface withnpuncturesF1,n, we show that the Hatcher–Thurston complex $${\fancyscript{HT}(F_{1,n})}$$ is hyperbolic. For the genus 2 closed surfaceF2, we show that the Hatcher–Thurston complex $${\fancyscript{HT}(F_{2})}$$ is strongly relatively hyperbolic with respect to a family of its subspaces {Xγ}, whereγranges over all separating curves ofF2, and eachXγis isometric to the product of two Farey graphs.