THE CANCELLATION NORM AND THE GEOMETRY OF BI-INVARIANT WORD METRICS
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...
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| Veröffentlicht in: | Glasgow mathematical journal 2016-01, Vol.58 (1), p.153-176 |
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| container_title | Glasgow mathematical journal |
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| creator | BRANDENBURSKY, MICHAEL GAL, ŚWIATOSŁAW R. KĘDRA, JAREK MARCINKOWSKI, MICHAŁ |
| description | 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. |
| doi_str_mv | 10.1017/S0017089515000129 |
| format | Article |
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| language | eng |
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| source | Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; Cambridge University Press Journals Complete |
| subjects | Algorithms Cancellation Construction Geometry Graphs Mathematical models Norms Origins Studies Subgroups |
| title | THE CANCELLATION NORM AND THE GEOMETRY OF BI-INVARIANT WORD METRICS |
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