Given an irreducible, end-periodic homeomorphism $f:S\to S$ of a surface with finitely many ends, all accumulated by genus, the mapping torus, $M_f$, is the interior of a compact, irreducible, atoroidal 3-manifold $\text{◂◽.▸}{\overline{M}}_f$ with incompressible boundary. Our main result is an upper bound on the infimal hyperbolic volume of $\text{◂◽.▸}{\overline{M}}_f$ in terms of the translation length of $f$ on the pants graph of $S$. This builds on work of Brock and Agol in the finite-type setting. We also construct a broad class of examples of irreducible, end-periodic homeomorphisms and use them to show that our bound is asymptotically sharp.

中文翻译：

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端周期同胚和映射 tori 的体积

给定一个不可约的、周期末同胚$F:\mathrm{小号}\to \mathrm{小号}$具有有限多个端点的曲面，全部由属累积，映射环面，${米}_F$, 是一个紧凑的、不可约的、超环面 3 流形的内部$\text{◂◽.▸}{\overline{米}}_F$具有不可压缩的边界。我们的主要结果是最后一个双曲体积的上界$\text{◂◽.▸}{\overline{米}}_F$在翻译长度方面$F$在裤子图上$\mathrm{小号}$. 这建立在 Brock 和 Agol 在有限类型设置中的工作之上。我们还构造了一大类不可约的、端周期同胚的例子，并用它们来证明我们的界限是渐近尖锐的。