THE CANCELLATION NORM and the GEOMETRY of BI-INVARIANT WORD METRICS

Michael Brandenbursky, ͆wiatosŁaw R. Gal, Jarek Keędra, MichaŁ Marcinkowski

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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 languageEnglish
Pages (from-to)153-176
Number of pages24
JournalGlasgow Mathematical Journal
Volume58
Issue number1
DOIs
StatePublished - 1 Jan 2016
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics (all)

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