Abstract
We 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 bq-dichotomy and we prove it for many classes of groups of geometric origin.
| Original language | English |
|---|---|
| Pages (from-to) | 153-176 |
| Number of pages | 24 |
| Journal | Glasgow Mathematical Journal |
| Volume | 58 |
| Issue number | 01 |
| Early online date | 21 Jul 2015 |
| DOIs | |
| Publication status | Published - Jan 2016 |
Bibliographical note
Footnotes: M. M. was partially supported by a scholarship from the Polish Science Foundation. SG and MM were partially supported by Polish National Science Center (NCN) grant 2012/06/A/ST1/00259.Fingerprint
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Jarek Kedra
- School of Natural & Computing Sciences, Mathematical Science - Personal Chair
Person: Academic