Klein bottles in lens spaces
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866910411274584064 |
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| author | Geiges, Hansjörg Thies, Norman |
| author_facet | Geiges, Hansjörg Thies, Norman |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_04909 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Klein bottles in lens spaces Geiges, Hansjörg Thies, Norman Geometric Topology 57R40, 57K30, 57M99 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. |
| title | Klein bottles in lens spaces |
| topic | Geometric Topology 57R40, 57K30, 57M99 |
| url | https://arxiv.org/abs/2205.04909 |