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

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

doi:https://doi.org/10.1017/S0017089515000129

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

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

Research output: Contribution to journal › Article › peer-review

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	American English
Pages (from-to)	153-176
Number of pages	24
Journal	Glasgow Mathematical Journal
Volume	58
Issue number	1
DOIs	https://doi.org/10.1017/S0017089515000129
State	Published - 1 Jan 2016
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics

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https://doi.org/10.1017/S0017089515000129

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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.",

author = "Michael Brandenbursky and Gal, {͆wiatos{\L}aw R.} and Jarek Ke{\c e}dra and Micha{\L} Marcinkowski",

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AU - Marcinkowski, MichaŁ

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

Abstract

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