 

David Fisher, Dave Witte Morris, and Kevin Whyte
Nonergodic actions, cocycles and superrigidity


Published: 
August 31, 2004 
Keywords: 
Borel action, nonergodic, ergodic component, Borel cocycle, superrigidity, von Neumann Selection Theorem 
Subject: 
28D15 


Abstract
This paper proves various results concerning nonergodic actions
of locally compact groups and particularly Borel cocycles defined
over such actions. The general philosophy is to reduce the study
of the cocycle to the study of its restriction to each ergodic
component of the action, while being careful to show that all
objects arising in the analysis depend measurably on the ergodic
component. This allows us to prove a version of the superrigidity
theorems for cocycles defined over nonergodic actions.


Acknowledgements
This research was partially supported by the National Science Foundation (grants DMS0226121, DMS0100438, and DMS0204576). The first author was also partially supported by a PSCCUNY grant.


Author information
David Fisher:
Department of Mathematics and Computer Science, Lehman College  CUNY, 250 Bedford Park Boulevard W., Bronx, NY 10468
dfisher@lehman.cuny.edu
http://comet.lehman.cuny.edu/fisher/
Dave Witte Morris:
Department of Mathematics and Computer Science, University of Lethbridge, 4401 University Drive, Lethbridge, AB, T1K 3M4, Canada
Dave.Morris@uleth.ca
http://people.uleth.ca/~dave.morris/
Kevin Whyte:
Department of Mathematics, University of Illinois at Chicago, 851 S. Morgan Street, Chicago, IL 606077045
kwhyte@math.uic.edu
http://www2.math.uic.edu/~kwhyte/

