穿孔表面填充对的长度

arXiv - MATH - Geometric Topology Pub Date : 2024-09-09 DOI:arxiv-2409.05483

Bhola Nath Saha, Bidyut Sanki

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引用次数: 0

摘要

如果在属$g$且有$n$穿刺的曲面$S_{g,n}$上的一对简单闭合曲线$(\alpha, \beta)$的补集是拓扑圆盘和一次穿刺圆盘的不相交联合，那么这对曲线被称为填充对。本文研究了一次穿刺双曲面上填充对的长度。特别是，我们发现了填充对长度的下限，它只取决于曲面的拓扑结构。

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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Length of Filling Pairs on Punctured Surface

A pair $(\alpha, \beta)$ of simple closed curves on a surface $S_{g,n}$ of genus $g$ and with $n$ punctures is called a filling pair if the complement of the union of the curves is a disjoint union of topological disks and once punctured disks. In this article, we study the length of filling pairs on once-punctured hyperbolic surfaces. In particular, we find a lower bound of the length of filling pairs which depends only on the topology of the surface.

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arXiv - MATH - Geometric Topology

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