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math.GR2026
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.
math.GR2024
Are free groups of different ranks bi-invariantly quasi-isometric?
Jarek KÄdra, 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.
math.GR2024
On the geometry and bounded cohomology of racks and quandles
Jarek KÄdra
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…