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math.GR2018
An extreme counterexample to the Lubotzky--Weiss conjecture
Masato Mimura
In 1993, Lubotzky and Weiss conjectured that if a compact group admits two finitely generated dense subgroups, one of which is amenable and the other has Kazhdan's property (T), th…
math.GR2018
Amenability versus non-exactness of dense subgroups of a compact group
Masato Mimura
Given a countable residually finite group, we construct a compact group K and two elements w and u of K with the following properties: The group generated by w and the cube of u is…
math.GR2018
Group approximation in Cayley topology and coarse geometry, Part II: Fibered coarse embeddings
Masato Mimura, Hiroki Sako
The objective of this series is to study metric geometric properties of disjoint unions of amenable Cayley graphs by group properties of the Cayley accumulation points in the space…