Special issue: 2014 KOOK-TAPU Workshop on Knot Theory and Related TopicsNo Access

On knotted real projective planes

Yongju Bae

Department of Mathematics, College of Natural Sciences, Kyungpook National University, Daegu 702-701, Korea

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Seonmi Choi

Department of Mathematics, College of Natural Sciences, Kyungpook National University, Daegu 702-701, Korea

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, and

Akio Kawauchi

Osaka City University Advanced Mathematical Institute, Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan

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https://doi.org/10.1142/S0218216515400118Cited by:0 (Source: Crossref)

Abstract

Let be a hyperbolic transformation. Let B be a new band attaching to L such that is also a hyperbolic transformation. In this paper, we will study the relationship between the realizing surfaces and . If B is a noncoherent band to both L and such that is defined, then and are ambient isotopic, where RP² is one of the standard real projective planes. We will study the triviality of because as an application, RP² can untangle some knotted sphere with suitable conditions, when it is attached to by the connected sum.

Keywords:

AMSC: 57M25, 57M27

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