We study biinvariant word metrics on groups. We provide an efficient
algorithm for computing the biinvariant word norm on a finitely
generated free group and we construct an isometric embedding of a
locally compact tree into the biinvariant 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
bq-dichotomy and we prove it for many classes of groups of geometric
origin.

Original language | English GB |
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State | Published - 2013 |
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- Mathematics - Geometric Topology
- Mathematics - Group Theory