Cancelation norm and the geometry of biinvariant word metrics

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.

arXiv comment33 pages, updated version

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Cited by in corpus (3)

• Concordance group and stable commutator length in braid groups
• On the Minimum Area of Null Homotopies of Curves Traced Twice
• The Khinchin-Kahane and Levy inequalities for abelian metric groups, and transfer from normed (abelian semi)groups to Banach spaces