39 citations · 126 across the 27 of their papers we have counts for
5 papers · 1 filter
Torsion in asymptotic cones of free groups
Jarek Kędra, Assaf Libman, Zipei Nie
We prove that the asymptotic cone of any non-abelian free group equipped with the bi-invariant word metric has elements of order 2.
Are free groups of different ranks bi-invariantly quasi-isometric?
Jarek Kędra, Assaf Libman
We prove that a homomorphism between free groups of finite rank equipped with the bi-invariant word metrics is a quasi-isometry if and only if it is an isomorphism.
On the geometry and bounded cohomology of racks and quandles
Jarek Kędra
We introduce and investigate a natural family of metrics on connected components of a rack. The metrics are closely related to certain bi-invariant metrics on the group of inner au…
Directional asymptotic cones of groups equipped with bi-invariant metrics
Jarek Kędra, Assaf Libman
Given a bi-invariant metric on a group, we construct a version of an asymptotic cone without using ultrafilters. The new construction, called the directional asymptotic cone, is a…
Finite index subgroups in Chevalley groups are bounded: an addendum to "On bi-invariant word metrics"
Światosław R. Gal, Jarek Kędra, Alexander A. Trost
We prove that finite index subgroups in S-arithmetic Chevalley groups are bounded.