6 papers
Borel dimension growth and hyperfiniteness
Jan Grebík, Andrew S. Marks, Václav Rozhoň +1
We show that every increasing union of Borel graphs of pointwise volume growth at most is hyperfinite, where is the unique real root of $(1 - γ)^3…
Hyperfiniteness of bounded-to-one actions of commutative monoids
Forte Shinko, Felix Weilacher, Jing Yu
A theorem of Dougherty--Jackson--Kechris states that any equivalence relation generated by a single Borel function is hypersmooth. A well-known open problem is whether this can be…
Realizations of countable Borel equivalence relations
Joshua Frisch, Alexander Kechris, Forte Shinko +1
We study topological realizations of countable Borel equivalence relations, including realizations by continuous actions of countable groups, with additional desirable properties.…
Hyperfiniteness for group actions on trees
Srivatsav Kunnawalkam Elayavalli, Koichi Oyakawa, Forte Shinko +1
We identify natural conditions for a countable group acting on a countable tree which imply that the orbit equivalence relation of the induced action on the Gromov boundary is Bore…
Hyper-hyperfiniteness and complexity
Joshua Frisch, Forte Shinko, Zoltan Vidnyanszky
We show that if there exists a countable Borel equivalence relation which is hyper-hyperfinite but not hyperfinite then the complexity of hyperfinite countable Borel equivalence re…
Asymptotic dimension and hyperfiniteness of generic Cantor actions
Sumun Iyer, Forte Shinko
We show that for a countable discrete group which is locally of finite asymptotic dimension, the generic continuous action on Cantor space has hyperfinite orbit equivalence relatio…