Aut-invariant norms and Aut-invariant quasimorphisms on free and surface groups Academic Article uri icon


  • Abstract: Let $ F_n $ be a free group on $ n $ generators and $\Gamma_g $ the surface group of genus $ g $. We consider two particular generating sets: the set of all primitive elements in $ F_n $ and the set of all simple loops in $\Gamma_g $. We give a complete characterization of distorted and undistorted elements in the corresponding $ Aut $-invariant word metrics. In particular, we reprove Stallings theorem and answer a question of Danny Calegari about the growth of simple loops. In addition, we construct infinitely many …

publication date

  • January 1, 2017