SMALL CURVATURE SURFACES IN HYPERBOLIC 3-MANIFOLDS

Author:

LEININGER CHRISTOPHER J.1

Affiliation:

1. Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green St., Urbana. IL, 61801, USA

Abstract

In a paper of Menasco and Reid, it is conjectured that there exist no hyperbolic knots in S3 for which the complement contains a closed embedded totally geodesic surface. In this note, we show that one can get "as close as possible" to a counter-example. Specifically, we construct a sequence of hyperbolic knots {Kn} with complements containing closed embedded essential surfaces having principal curvatures converging to zero as n tends to infinity. We also construct a family of two-component links for which the complements contain closed embedded totally geodesic surfaces of arbitrarily large genera. In addition, we prove that a closed embedded surface with sufficiently small principal curvatures is not only quasi-Fuchsian (a result of Thurston's), but it is also either acylindrical or the boundary of a twisted I-bundle.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Reference31 articles.

1. On Irreducible 3-Manifolds Which are Sufficiently Large

2. Three dimensional manifolds, Kleinian groups and hyperbolic geometry

3. Dehn Surgery on Knots

4. W. Menasco and A. Reid, Topology '90 (Columbus, OH, 1990), 215–226, Ohio State University Mathematical Research Institute Publications 1 (de Gruyter, Berlin, 1992) pp. 215–226.

5. Toroidally alternating knots and links

Cited by 12 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3