UNKNOTTING ORIENTABLE SURFACES IN THE 4-SPHERE

Author:

HILLMAN JONATHAN A.1,KAWAUCHI AKIO2

Affiliation:

1. School of Mathematics and Statistics, The University of Sydney, Sydney, N.S.W. 2006, Australia

2. Department of Mathematics, Osaka City University Sugimoto, Sumiyoshi-ku, Osaka, 558, Japan

Abstract

We show that a topologically locally flat embedding of a closed orientable surface in the 4-sphere is isotopic to one whose image lies in the equatorial 3-sphere if and only if its exterior has an infinite cyclic fundamental group.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Cited by 8 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. Smooth Homotopy 4-Sphere;WSEAS TRANSACTIONS ON MATHEMATICS;2023-09-26

2. Embedded surfaces with infinite cyclic knot group;Geometry & Topology;2023-05-16

3. Ribbonness of a stable-ribbon surface-link, I. A stably trivial surface-link;Topology and its Applications;2021-09

4. Bridge trisections of knotted surfaces in ⁴;Transactions of the American Mathematical Society;2017-05-30

5. A chord diagram of a ribbon surface-link;Journal of Knot Theory and Its Ramifications;2015-09

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