在细曲线图上近似稳定翻译长度
Approximating stable translation lengths on fine curve graphs
AI总结：
本文研究了在细曲线图上同胚的稳定翻译长度，并证明其与有限近似在非分离曲线图上的稳定翻译长度的关系，指出上界不总是最大值。
摘要：
我们研究了表面同胚在细非分离曲线图上的稳定翻译长度，并将其与有限近似（相对于有限不变集的映射类）在非分离曲线图上的稳定翻译长度进行比较。我们证明了具有稠密周期点集的同胚的稳定翻译长度是其近似的稳定翻译长度的上界，并且稳定翻译长度在细胞状扩展下保持不变。我们推导出，紧致流形的同胚的稳定翻译长度是其有限近似的稳定翻译长度的上界。我们通过证明映射类在非分离曲线图上的稳定翻译长度是有理数，展示了上界不总是最大值。
英文摘要：
We study the stable translation length of homeomorphisms of a surface acting on the fine nonseparating curve graph and compare it to the stable translation lengths of its finite approximations - mapping classes relative to a finite invariant set - acting on the nonseparating curve graph. We prove that the stable translation length of a homeomorphism with a dense set of periodic points is the supremum of the stable translation lengths of its approximations, and that the stable translation length is preserved under cell-like extensions. We deduce that homotopically triv ial homeomorphisms of the torus have stable translation length which is the supremum of the stable translation lengths of their finite approximations. We show that the supremum is not always a maximum, by proving that the stable translation length of a mapping class acting on the nonseparating curve graph is rational.
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