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2020 Immersed Möbius bands in knot complements
Mark C Hughes, Seungwon Kim
Algebr. Geom. Topol. 20(2): 1059-1072 (2020). DOI: 10.2140/agt.2020.20.1059

Abstract

We study the 3–dimensional immersed crosscap number of a knot, which is a nonorientable analogue of the immersed Seifert genus. We study knots with immersed crosscap number 1, and show that a knot has immersed crosscap number 1 if and only if it is a nontrivial (2p,q)–torus or (2p,q)–cable knot. We show that unlike in the orientable case the immersed crosscap number can differ from the embedded crosscap number by arbitrarily large amounts, and that it is neither bounded below nor above by the 4–dimensional crosscap number.

Citation

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Mark C Hughes. Seungwon Kim. "Immersed Möbius bands in knot complements." Algebr. Geom. Topol. 20 (2) 1059 - 1072, 2020. https://doi.org/10.2140/agt.2020.20.1059

Information

Received: 15 January 2019; Revised: 3 September 2019; Accepted: 16 January 2020; Published: 2020
First available in Project Euclid: 30 April 2020

zbMATH: 07195385
MathSciNet: MR4092320
Digital Object Identifier: 10.2140/agt.2020.20.1059

Subjects:
Primary: 57M25, 57M27
Secondary: 57M35

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.20 • No. 2 • 2020
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