当前位置: X-MOL 学术J. Topol. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
End-periodic homeomorphisms and volumes of mapping tori
Journal of Topology ( IF 0.8 ) Pub Date : 2023-01-06 , DOI: 10.1112/topo.12277
Elizabeth Field 1 , Heejoung Kim 2 , Christopher Leininger 3 , Marissa Loving 4
Affiliation  

Given an irreducible, end-periodic homeomorphism f:SS$f: S \rightarrow S$ of a surface with finitely many ends, all accumulated by genus, the mapping torus, Mf$M_f$, is the interior of a compact, irreducible, atoroidal 3-manifold ◂◽.▸M¯f$\overline{M}_f$ with incompressible boundary. Our main result is an upper bound on the infimal hyperbolic volume of ◂◽.▸M¯f$\overline{M}_f$ in terms of the translation length of f$f$ on the pants graph of S$S$. 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:

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:小号小号$f: S \右箭头 S$具有有限多个端点的曲面,全部由属累积,映射环面,F$M_f$, 是一个紧凑的、不可约的、超环面 3 流形的内部◂◽.▸¯F$\overline{M}_f$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◂◽.▸¯F$\overline{M}_f$在翻译长度方面F$f$在裤子图上小号$新元$. 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。
更新日期:2023-01-10
down
wechat
bug