THE CANCELLATION NORM AND THE GEOMETRY OF BI-INVARIANT WORD METRICS

MICHAEL BRANDENBURSKY, ŚWIATOSŁAW R. GAL, JAREK KĘDRA, MICHAŁ MARCINKOWSKI
2015 Glasgow Mathematical Journal  
AbstractWe study bi-invariant word metrics on groups. We provide an efficient algorithm for computing the bi-invariant word norm on a finitely generated free group and we construct an isometric embedding of a locally compact tree into the bi-invariant Cayley graph of a nonabelian free group. We investigate the geometry of cyclic subgroups. We observe that in many classes of groups, cyclic subgroups are either bounded or detected by homogeneous quasimorphisms. We call this property the
more » ... perty the bq-dichotomy and we prove it for many classes of groups of geometric origin.
doi:10.1017/s0017089515000129 fatcat:jfgh3xvbgbfzdlbcqihxdsuphy