Speaker：Guohua Zhang（Fudan University）

Time：2022-03-28 15:00

Location：Tencent Meeting ID：804 753 961（No Password）

Abstract: Let a countable discrete group G act on a zero-dimensional compact metric space X. We say that the action admits comparison if for any clopen sets A and B, the condition, that for every G-invariant measure m on X we have the sharp inequality m(A)< m(B), implies that A is subequivalent to B, that is, there exists a finite clopen partition {A1, ..., Ak} for A, and elements g1, ..., gk in G such that g1(A1), ..., gk(Ak) are disjoint clopen subsets of B. We prove this property for actions of groups whose every finitely generated subgroup has subexponential growth. This is a joint work with Professor Tomasz Downarowicz.