Klein bottles in lens spaces

Hansjörg Geiges; Norman Thies

doi:10.2140/involve.2023.16.621

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arXiv · 2205.04909

Klein bottles in lens spaces

Hansjörg Geiges·Norman Thies

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Abstract

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 $L(4n,2n\pm 1)$ only. We describe four explicit realisations of these embeddings.

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BibTeX RIS

Hansjörg Geiges, Norman Thies. 2022-05-10. Klein bottles in lens spaces. https://doi.org/10.2140/involve.2023.16.621

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