End-periodic homeomorphisms and volumes of mapping tori

Pub Date : 2023-01-06 DOI:10.1112/topo.12277

Elizabeth Field, Heejoung Kim, Christopher Leininger, Marissa Loving

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引用次数: 7

Abstract

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 ${\bar{M}}_{f}$ with incompressible boundary. Our main result is an upper bound on the infimal hyperbolic volume of ${\bar{M}}_{f}$ 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.

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映射tori的端周期同胚与体积

给定一个不可约的末端周期同胚f:S→ S$f:S\rightarrowS$的一个具有有限多个末端的曲面，所有末端都由亏格累加，映射环面Mf$M_f$是一个紧致的、不可约的，阿托向3流形M'f$\overline{M}_f具有不可压缩边界的$。我们的主要结果是M’f$\overline的下微双曲体积的上界{M}_f$在S$S$的裤子图上的f$f$的平移长度。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是渐近尖锐的。

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