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Mathematics > Geometric Topology

arXiv:1804.02654 (math)
[Submitted on 8 Apr 2018 (v1), last revised 28 May 2022 (this version, v12)]

Title:Ribbonness of a stable-ribbon surface-link, I. A stably trivial surface-link

Authors:Akio Kawauchi
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Abstract:There is a question asking whether a handle-irreducible summand of every stable-ribbon surface-link is a unique ribbon surface-link. This question for the case of a trivial surface-link is affirmatively answered. That is, a handle-irreducible summand of every stably trivial surface-link is only a trivial 2-link. By combining this result with an old result of F. Hosowaka and the author that every surface-knot with infinite cyclic fundamental group is a stably trivial surface-knot, it is concluded that every surface-knot with infinite cyclic fundamental group is a trivial (i.e., an unknotted) surface-knot.
Comments: This is the part I on "Ribbonness of a stable-ribbon surface-link". New revision of Section 3 is added as the separated paper "Uniqueness of an orthogonal 2-handle pair on a surface-link"
Subjects: Geometric Topology (math.GT)
MSC classes: 57Q45 (Primary), 57M15, 57N13 (Secondary)
Cite as: arXiv:1804.02654 [math.GT]
  (or arXiv:1804.02654v12 [math.GT] for this version)
  https://doi.org/10.48550/arXiv.1804.02654

Submission history

From: Akio Kawauchi [view email]
[v1] Sun, 8 Apr 2018 08:53:59 UTC (1,175 KB)
[v2] Thu, 19 Apr 2018 05:17:59 UTC (1,175 KB)
[v3] Mon, 30 Apr 2018 12:31:17 UTC (1,312 KB)
[v4] Thu, 17 May 2018 02:32:34 UTC (5,113 KB)
[v5] Tue, 22 May 2018 13:01:51 UTC (5,110 KB)
[v6] Thu, 24 May 2018 07:37:57 UTC (4,521 KB)
[v7] Tue, 5 Jun 2018 00:32:43 UTC (5,039 KB)
[v8] Tue, 19 Jun 2018 07:42:03 UTC (3,277 KB)
[v9] Tue, 23 Jul 2019 06:20:33 UTC (2,849 KB)
[v10] Tue, 29 Sep 2020 01:07:20 UTC (10,409 KB)
[v11] Fri, 23 Apr 2021 23:05:48 UTC (5,239 KB)
[v12] Sat, 28 May 2022 00:23:13 UTC (5,211 KB)
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