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- Title
Aut-invariant norms and Aut-invariant quasimorphisms on free and surface groups.
- Authors
Brandenbursky, Michael; Marcinkowski, Michał
- Abstract
Let Fn be the free group on n generators and g the surface group of genus g. We consider two particular generating sets: the set of all primitive elements in Fn and the set of all simple loops in 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 quasimorphisms on F² that are Aut.F²/-invariant. This answers an open problem posed by Miklós Abért.
- Subjects
FREE groups; FREE surfaces; FINITE simple groups; GENERATORS of groups
- Publication
Commentarii Mathematici Helvetici, 2019, Vol 94, Issue 4, p661
- ISSN
0010-2571
- Publication type
Article
- DOI
10.4171/CMH/470