Klein bottles in lens spaces

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.

14 pages, 8 figures; v2: minor changes, one figure added

References in corpus (1)

• Seifert fibrations of lens spaces over non-orientable bases

Cited by in corpus (1)

• Bott-integrable Reeb flows on 3-manifolds