Geodesic
Immersed Möbius bands in knot complements
Hughes, Mark1 ; Kim, Seungwon2
1Department of Mathematics, Brigham Young University, Provo, UT, United States
2Center for Geometry and Physics, Institute for Basic Science (IBS), Pohang, South Korea
Algebraic and Geometric Topology, Tome 20 (2020) no. 2, pp. 1059-1072
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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.

DOI : 10.2140/agt.2020.20.1059
Classification : 57M25, 57M27, 57M35
Keywords: knots, Möbius bands, immersed surfaces

Hughes, Mark  1   ; Kim, Seungwon  2

1 Department of Mathematics, Brigham Young University, Provo, UT, United States
2 Center for Geometry and Physics, Institute for Basic Science (IBS), Pohang, South Korea 
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Hughes, Mark; Kim, Seungwon. Immersed Möbius bands in knot complements. Algebraic and Geometric Topology, Tome 20 (2020) no. 2, pp. 1059-1072. doi: 10.2140/agt.2020.20.1059

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