Lipschitz constants to curve complexes for punctured surfaces

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• 作者：Aaron D. Valdivia ^{avaldivia@flsouthern.edu}
• 关键词：Mapping class groups ; Moduli spaces ; Curve complex ; Pseudo-Anosov ; Lipschitz
• 刊名：Topology and its Applications
• 出版年：2017
• 出版时间：1 February 2017
• 年：2017
• 卷：216
• 期：Complete
• 页码：137-145
• 全文大小：720 K
• 卷排序：216

文摘

Given a surface Sg,nSg,n there is a map sys:Tg,n→Cg,nsys:Tg,n→Cg,n where Tg,nTg,n is the Teichmüller space with the Teichmüller metric, Cg,nCg,n is the curve complex with the standard metric, anddCg,n(sys(X),sys(Y))≤KdTg,n(X,Y)+C.dCg,n(sys(X),sys(Y))≤KdTg,n(X,Y)+C. We give asymptotic bounds for the minimal value of K   which we denote Kg,n≍1log⁡(|χg,n|) for sequences of surfaces with fixed genus and sequences of surfaces where the genus is a rational multiple of the punctures. This generalizes work of Gadre, Hironaka, Kent, and Leininger where they give the same asymptotic bounds for closed surfaces.