UW Rainwater Seminar
Spring 2011
Date: May 10 at 2:30
Location: UW
Padelford C-401
Speaker: Michael Hochman, Hebrew University and Microsoft Research
Title: Infinite measure preserving Z^d actions without smooth models
Abstract:
By a classical theorem of Krengel, if f is a map preserving an infinite, sigma-finite
measure, then it is measurably isomorphic to a diffeomorphism of a compact manifold preserving a
Borel measure. This fact is related to others which show that there is no good notion of entropy for
infinite measure preserving systems. It turns out that there do exist Z^d actions, d>1, which do not
have smooth models in the above sense. The obstruction involves a "slow entropy" invariant a-la
Katok and Thouvenot. I will discuss this result, starting from the classical results for
probability-preserving actions and infinite measure preserving transformations.