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Klein bottles
in lens spaces
Hansjörg Geiges and Norman Thies |
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Vol. 16 (2023), No. 4, 621–636
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Abstract |
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Bredon and Wood have given a complete answer to the embeddability question for nonorientable surfaces in lens spaces. They formulate their result in terms of a recursive formula that determines, for a given lens space, the minimal genus of embeddable nonorientable surfaces. Here we give a direct proof that, amongst lens spaces as target manifolds, the Klein bottle embeds into only. We describe four explicit realisations of these embeddings. |
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Keywords
Klein bottle, lens space, embedding, Seifert fibration
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Mathematical Subject Classification
Primary: 57R40, 57K30, 57M99
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Milestones
Received: 13 May 2022
Accepted: 11 August 2022
Published: 31 October 2023
Communicated by Colin Adams
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Authors |
| Hansjörg Geiges | |
| Mathematisches Institut Universität zu Köln Köln Germany |
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| Norman Thies | |
| Mathematisches Institut Universität zu Köln Köln Germany |
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| © 2023 MSP (Mathematical Sciences Publishers). |
