Cancellation norm and the geometry of bi-invariant word metrics

Michael Brandenbursky, Swiatoslaw Gal, Jarek Kedra, Michal Marcinkowski

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


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 languageEnglish
Pages (from-to)153-176
Number of pages24
JournalGlasgow Mathematical Journal
Issue number01
Early online date21 Jul 2015
Publication statusPublished - 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.


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