End-periodic homeomorphisms and volumes of mapping tori

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Topology 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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来源期刊

Journal of Topology 数学-数学

CiteScore

2.00

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Topology publishes papers of high quality and significance in topology, geometry and adjacent areas of mathematics. Interesting, important and often unexpected links connect topology and geometry with many other parts of mathematics, and the editors welcome submissions on exciting new advances concerning such links, as well as those in the core subject areas of the journal. The Journal of Topology was founded in 2008. It is published quarterly with articles published individually online prior to appearing in a printed issue.