Fixed point properties and second bounded cohomology of universal lattices on Banach space

Mathematics – Functional Analysis

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

This is the final version; 21 pages

Scientific paper

10.1515/CRELLE.2011.021

Let B be any Lp space for p in (1,infty) or any Banach space isomorphic to a Hilbert space, and k be a nonnegative integer. We show that if n is at least 4, then the universal lattice Gamma =SL_n (Z[x1,...,xk]) has property (F_B) in the sense of Bader--Furman--Gelander--Monod. Namely, any affine isometric action of Gamma on B has a global fixed point. The property of having (F_B) for all B above is known to be strictly stronger than Kazhdan's property (T). We also define the following generalization of property (F_B)$ for a group: the boundedness property of all affine quasi-actions on B. We name it property (FF_B) and prove that the group Gamma above also has this property modulo trivial part. The conclusion above in particular implies that the comparison map in degree two H^2_b (Gamma; B) \to H^2(Gamma; B) from bounded to ordinary cohomology is injective, provided that the associated linear representation does not contain the trivial representation.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Fixed point properties and second bounded cohomology of universal lattices on Banach space 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 Fixed point properties and second bounded cohomology of universal lattices on Banach space, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Fixed point properties and second bounded cohomology of universal lattices on Banach space will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-512716

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.