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

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

Let B be any Lp space for p ∈ (1, ∞) or any Banach space isomorphic to a Hilbert space, and k ≧ 0 be integer. We show that if n ≧ 4, then the universal lattice Γ = SLn(ℤ[x1,..., xk]) has property (FB) in the sense of Bader-Furman-Gelander-Monod. Namely, any affine isometric action of Γ on B has a global fixed point. The property of having (FB) for all B above is known to be strictly stronger than Kazhdan's property (T). We also define the following generalization of property (FB) for a group: the boundedness property of all affine quasi-actions on B. We name it property (FFB) and prove that the group Γ above also has this property modulo trivial part. The conclusion above implies that the comparison map in degree two H b2 (Γ;B) → H2(ΓB) from bounded to ordinary cohomology is injective, provided that the associated linear representation does not contain the trivial representation.

Original languageEnglish
Pages (from-to)115-134
Number of pages20
JournalJournal fur die Reine und Angewandte Mathematik
Issue number653
DOIs
Publication statusPublished - 2011 Apr 1
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Fixed point properties and second bounded cohomology of universal lattices on Banach spaces'. Together they form a unique fingerprint.

Cite this