ON TUNNEL NUMBER ONE KNOTS THAT ARE NOT (1, n)-Reference-Cited by-同舟云学术

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ON TUNNEL NUMBER ONE KNOTS THAT ARE NOT (1, n)

Published:2011-04 Issue:04 Volume:20 Page:609-615
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

JOHNSON JESSE¹,THOMPSON ABIGAIL²

Affiliation:

1. Department of Mathematics, Oklahoma State University, Stillwater, OK 74078, USA

2. Department of Mathematics, University of California, Davis, CA 95616, USA

Abstract

We show that the bridge number of a tunnel number t knot in S3 with respect to an unknotted genus t surface is bounded below by a function of the distance of the Heegaard splitting induced by the t tunnels. It follows that for any natural number n, there is a tunnel number one knot in S3 that is not (1, n).

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216511009376

Reference7 articles.

1. 3-Manifolds as viewed from the curve complex

2. Geometry of the complex of curves I: Hyperbolicity

3. Heegaard structures of negatively curved 3-manifolds

4. Examples of tunnel number one knots which have the property ‘1 + 1 = 3’

Cited by 3 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

1. Double branched covers of tunnel number one knots;Geometriae Dedicata;2020-06-22

2. On composite types of tunnel number two knots;Journal of Knot Theory and Its Ramifications;2015-02

3. Tunnel number degeneration under the connected sum of prime knots;Topology and its Applications;2013-06

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