Cancelation norm and the geometry of biinvariant word metrics

Michael Brandenbursky; Światosław R. Gal; Jarek Kędra; Michał Marcinkowski

doi:10.1017/s0017089515000129

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arXiv · 1310.2921

Cancelation norm and the geometry of biinvariant word metrics

Michael Brandenbursky·Światosław R. Gal·Jarek Kędra·Michał Marcinkowski

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Abstract

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.

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Michael Brandenbursky, Światosław R. Gal, Jarek Kędra, Michał Marcinkowski. 2013-10-10. Cancelation norm and the geometry of biinvariant word metrics. https://doi.org/10.1017/s0017089515000129

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