62 citations · 280 across the 23 of their papers we have counts for
18 papers · 1 filter
On treeings arising from HNN extensions
Yoshikata Kida
For certain HNN extensions including Baumslag-Solitar groups, a treeing is constructed from their certain probability-measure-preserving actions. This is a treeing of a quotient gr…
Groups with infinite FC-center have the Schmidt property
Yoshikata Kida, Robin Tucker-Drob
We show that every countable group with infinite FC-center has the Schmidt property, i.e., admits a free, ergodic, measure-preserving action on a standard probability space such th…
Splitting in orbit equivalence, treeable groups, and the Haagerup property
Yoshikata Kida
Let be a discrete countable group and its central subgroup with treeable. We show that for any treeable action of on a standard probability space , the group…
Stable actions of central extensions and relative property (T)
Yoshikata Kida
Let us say that a discrete countable group is stable if it has an ergodic, free, probability-measure-preserving and stable action. Let G be a discrete countable group with a centra…
Inner amenable groups having no stable action
Yoshikata Kida
We construct inner amenable and ICC groups having no ergodic, free, probability-measure-preserving and stable action. This solves a problem posed by Jones-Schmidt in 1987.
Stability in orbit equivalence for Baumslag-Solitar groups and Vaes groups
Yoshikata Kida
A measure-preserving action of a discrete countable group on a standard probability space is called stable if the associated equivalence relation is isomorphic to its direct produc…
Invariants of orbit equivalence relations and Baumslag-Solitar groups
Yoshikata Kida
To an ergodic, essentially free and measure-preserving action of a non-amenable Baumslag-Solitar group on a standard probability space, a flow is associated. The isomorphism class…
Automorphisms of the Torelli complex for the one-holed genus two surface
Yoshikata Kida, Saeko Yamagata
Let S be a connected, compact and orientable surface of genus two having exactly one boundary component. We study automorphisms of the Torelli complex for S, and describe any isomo…
Examples of amalgamated free products and coupling rigidity
Yoshikata Kida
We present amalgamated free products satisfying coupling rigidity with respect to the automorphism group of the associated Bass-Serre tree. As an application, we obtain orbit equiv…
The co-Hopfian property of surface braid groups
Yoshikata Kida, Saeko Yamagata
Let g and n be integers at least two, and let G be the pure braid group with n strands on a closed orientable surface of genus g. We describe any injective homomorphism from a fini…
Commensurators of surface braid groups
Yoshikata Kida, Saeko Yamagata
We prove that if g and n are integers at least two, then the abstract commensurator of the braid group with n strands on a closed orientable surface of genus g is naturally isomorp…
Injections of the complex of separating curves into the Torelli complex
Yoshikata Kida
We show that for all but finitely many compact orientable surfaces, any superinjective map from the complex of separating curves into the Torelli complex is induced by an element o…
The co-Hopfian property of the Johnson kernel and the Torelli group
Yoshikata Kida
For all but finitely many compact orientable surfaces, we show that any superinjective map from the complex of separating curves into itself is induced by an element of the extende…
Automorphisms of the Torelli complex and the complex of separating curves
Yoshikata Kida
We compute the automorphism groups of the Torelli complex and the complex of separating curves for all but finitely many compact orientable surfaces. As an application, we show tha…
Rigidity of amalgamated free products in measure equivalence
Yoshikata Kida
A discrete countable group Γis said to be ME rigid if any discrete countable group that is measure equivalent to Γis virtually isomorphic to Γ. In this paper, we construct ME rigid…
Measure equivalence rigidity of the mapping class group
Yoshikata Kida
We show that the mapping class group of a compact orientable surface with higher complexity has the following extreme rigidity in the sense of measure equivalence: if the mapping c…
Orbit equivalence rigidity for ergodic actions of the mapping class group
Yoshikata Kida
We establish orbit equivalence rigidity for any ergodic, essentially free and measure-preserving action on a standard Borel space with a finite positive measure of the mapping clas…
The mapping class group from the viewpoint of measure equivalence theory
Yoshikata Kida
We obtain some classification result for the mapping class groups of compact orientable surfaces in terms of measure equivalence. In particular, the mapping class groups of differe…