Event № 161
It is well known that for actions of amenable groups entropy is monotone decreasing under factor maps. In this talk, I will show that this fails in a very strong way for actions of non-amenable groups. Specifically, if G is a countable non-amenable group then there exists a finite integer n with the following property: for every pmp action of G on (X, \mu) there is a G-invariant probability measure \nu on n^G such that the action of G on (n^G, \nu) factors onto the action of G on (X, \mu). For many non-amenable groups, n can be chosen to be 4 or smaller. We also obtain a similar result for continuous actions on compact metric spaces and continuous factor maps.