Effective length-projection bounds for hyperbolic 3-manifolds diffeomorphic to S × R $S\times \mathbb {R}$

IF 1.6 2区数学 Q2 MATHEMATICS

Journal of Topology Pub Date : 2026-08-20 DOI:10.1112/topo.70096

Gabriele Viaggi

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引用次数: 0

Abstract

We give a formula with explicit constants relating the subsurface projection $d_{Y} (ν^{-}, ν^{+})$ of the end invariants $ν^{-}, ν^{+}$ of a hyperbolic 3-manifold $Q$ diffeomorphic to $S \times R$ and the length of the geodesic representative in $Q$ of the multicurve $\partial Y$ . This makes effective and computable the large projections versus short curves relation proved by Minsky. We give an application to closed hyperbolic 3-manifolds fibering over the circle providing a geometric analog of the uniform projection bound in fibered faces of Minsky and Taylor.

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S × R $S\乘以\mathbb {R}$的微分同态双曲3-流形的有效长度-投影界

我们给出了一个公式，其中有关于地下投影d Y （ν−）的显式常数，ν +) $d_Y(\nu ^-,\nu ^+)$末不变量ν−，双曲三流形Q $Q$与S × R微分同态$S\times \mathbb {R}$的ν + $\nu ^-,\nu ^+$和测地线代表的长度多元曲线∂Y $\partial Y$的Q $Q$中。这使得明斯基证明的大投影与短曲线的关系变得有效和可计算。给出了在圆上纤维化的闭双曲3流形的一个应用，给出了Minsky和Taylor纤维化面的均匀投影界的一个几何类比。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.