Mathematics – Group Theory
Scientific paper
2005-09-22
Geom. Funct. Anal. 17(3) (2007), 770-792
Mathematics
Group Theory
26 pages, no figure. To appear in Geom. Funct. Anal
Scientific paper
10.1007/s00039-007-0604-0
We study growth of 1-cocycles of locally compact groups, with values in unitary representations. Discussing the existence of 1-cocycles with linear growth, we obtain the following alternative for a class of amenable groups G containing polycyclic groups and connected amenable Lie groups: either G has no quasi-isometric embedding into Hilbert space, or G admits a proper cocompact action on some Euclidean space. On the other hand, noting that almost coboundaries (i.e. 1-cocycles approximable by bounded 1-cocycles) have sublinear growth, we discuss the converse, which turns out to hold for amenable groups with "controlled" Folner sequences; for general amenable groups we prove the weaker result that 1-cocycles with sufficiently small growth are almost coboundaries. Besides, we show that there exist, on a-T-menable groups, proper cocycles with arbitrary small growth.
Cornulier Yves de
Tessera Romain
Valette Alain
No associations
LandOfFree
Isometric group actions on Hilbert spaces: growth of cocycles does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Isometric group actions on Hilbert spaces: growth of cocycles, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Isometric group actions on Hilbert spaces: growth of cocycles will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-503768