The mapping class group of a nonorientable surface is quasi-isometrically embedded in the mapping class group of the orientation double cover

  • Takuya Katayama

    Gakushuin University, Tokyo, Japan
  • Erika Kuno

    Osaka University, Osaka, Japan
The mapping class group of a nonorientable surface is quasi-isometrically embedded in the mapping class group of the orientation double cover cover
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Abstract

Let be a connected nonorientable surface with or without boundary and punctures, and be the orientation double covering. It has previously been proved that induces an embedding with one exception. In this paper, we prove that the injective homomorphism is a quasi-isometric embedding. The proof is based on the semihyperbolicity of , which has already been established. We also prove that the embedding induced by an inclusion of a pair of possibly nonorientable surfaces is a quasi-isometric embedding.

Cite this article

Takuya Katayama, Erika Kuno, The mapping class group of a nonorientable surface is quasi-isometrically embedded in the mapping class group of the orientation double cover. Groups Geom. Dyn. 18 (2024), no. 2, pp. 407–418

DOI 10.4171/GGD/776