Quasi-isometric embeddings from mapping class groups of nonorientable surfaces (Women in Mathematics)

Abstract

Classifying finitely generated groups by quasi-isometries is a key issue in geometric group theory: two groups are quasi-isometric if, roughly speaking, their word metrics are the same up to linear functions. It is known that the mapping group Mod(N) of a nonorientable surface N is a subgroup of the mapping group Mod(S) of its double covering orientable surface S. We show that the injective homomorphism is a quasi-isometric embedding. This is a joint work with Takuya Katayama