We investigate dynamical analogues of the $L^2$-Betti numbers for modules over integral
of a discrete sofic group. In particular, we use them to introduce some invariants for algebraicactions.
As an application, we give a dynamical characterization of Lueck's dimension-flatness.
Links:
[1] http://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/de/node/3444
[3] http://www.mpim-bonn.mpg.de/de/node/158