Mapping class groups and interpolating complexes: rank
Mapping class groups and interpolating complexes: rank
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发表时间：
2009
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通讯作者：
M. Mahan
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作者：
M. Mahan
抽象的。对曲面S和-2 ≤ <$≤ <$（S）构造了一类复杂度为<$的插值图C（S，<$）.当n =-2，-1，n（S）-1时，这些图分别与标号图、裤子图和曲线图拟等距。我们推广了层次的概念和Brock-Farb定理和Behrstock-Minsky定理，证明了C（S，S）的秩是r，即可以嵌入S中的复杂度大于r的子曲面的不相交副本的最大数量。插值图C（S，ξ）插值于裤子图和曲线图之间。
Abstract. A family of interpolating graphs C(S, ξ) of complexity ξ is constructed for a surface S and -2 ≤ ξ ≤ ξ(S). For ξ = -2,-1, ξ (S) -1 these specialize to graphs quasi-isometric to the marking graph, the pants graph and the curve graph respectively. We generalize the notion of a hierarchy and Theorems of Brock-Farb and Behrstock-Minsky to show that the rank of C(S, ξ) is rξ, the largest number of disjoint copies of subsurfaces of complexity greater than ξ that may be embedded in S. The interpolating graphs C(S, ξ) interpolate between the pants graph and the curve graph.