论文标题
曲线复合物中有效的测量学的超级效率
Super efficiency of efficient geodesics in the complex of curves
论文作者
论文摘要
我们表明，有效的测量学具有“超级效率”的强大特性。对于任何两个顶点，$ v，w \ in \ Mathcal {c}（s_g）$，在曲线的复合体中Arxiv：1408.4133），最多有一个明确的可计算列表，最多可{\ text d}^{（6G-6）} $ v_1 $ dertex的候选者。在本说明中，我们为此可计算列表建立了一个绑定，该列表独立于$ {\ text d} $ - 距离，仅取决于属 - 超级效率属性。证明依赖于曲线的相交数量与它们在曲线复合物中的距离之间的新相交生长不等式，以及对与交叉序列相关的点图的彻底分析。
We show that efficient geodesics have the strong property of "super efficiency". For any two vertices, $v , w \in \mathcal{C}(S_g)$, in the complex of curves of a closed oriented surface of genus $g \geq 2 $, and any efficient geodesic, $v = v_1 , \cdots , v_{\text d}=w$, it was previously established by Birman, Margalit and the second author (see arXiv:1408.4133) that there is an explicitly computable list of at most ${\text d}^{(6g-6)}$ candidates for the $v_1$ vertex. In this note we establish a bound for this computable list that is independent of ${\text d}$-distance and only dependent on genus -- the super efficiency property. The proof relies on a new intersection growth inequality between intersection number of curves and their distance in the complex of curves, together with a thorough analysis of the dot graph associated with the intersection sequence.
