On knotted real projective planes

Yongju Bae; Seonmi Choi; Akio Kawauchi

doi:10.1142/S0218216515400118

On knotted real projective planes

Yongju Bae, Seonmi Choi, Akio Kawauchi

Research output: Contribution to journal › Article › peer-review

Abstract

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

Original language	English
Article number	1540011
Journal	Journal of Knot Theory and its Ramifications
Volume	24
Issue number	10
DOIs	https://doi.org/10.1142/S0218216515400118
State	Published - 2 Sep 2015

Keywords

closed realizing surface
Hyperbolic transformation
realizing surface
ribbon 2-knot
ribbon knot
standard real projective planes

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

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T1 - On knotted real projective planes

AU - Bae, Yongju

AU - Choi, Seonmi

AU - Kawauchi, Akio

PY - 2015/9/2

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N2 - Let LB→ LB be a hyperbolic transformation. Let B be a new band attaching to L such that LBB→ LBU{B} is also a hyperbolic transformation. In this paper, we will study the relationship between the realizing surfaces F(LBB→ LBU{B}) and F(LBB→ LBU{B}). If B is a noncoherent band to both L and LB such that F(LBB→B LBU{B}) is defined, then F(LBB→ LB) RP2 and F(LBB→ LUL{B})RP2 are ambient isotopic, where RP2 is one of the standard real projective planes. We will study the triviality of F(LBB→ LBU{B}) because as an application, RP2 can untangle some knotted sphere F(LB→ LB) with suitable conditions, when it is attached to F(LB→ LB) by the connected sum.

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

KW - closed realizing surface

KW - Hyperbolic transformation

KW - realizing surface

KW - ribbon 2-knot

KW - ribbon knot

KW - standard real projective planes

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JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

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ER -

On knotted real projective planes

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