Cancelation norm and the geometry of biinvariant word metrics

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

Research output: Working paper/PreprintPreprint

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.
Original languageEnglish
StatePublished - 2013

Publication series

NameArxiv preprint

Keywords

  • Mathematics - Geometric Topology
  • Mathematics - Group Theory

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