Reduced 1-cohomology and relative property (T)

1 Reduced power operations in motivic cohomology

A 1-COHOMOLOGY CHARACTERIZATION OF PROPERTY (T) IN VON NEUMANN ALGEBRAS by JESSE PETERSON

We obtain a characterization of property (T) for von Neumann algebras in terms of 1-cohomology similar to the Delorme-Guichardet Theorem for groups. Throughout this paper N will denote a finite von Neumann algebra with a fixed normal faithful tracial state τ .

A 1-cohomology Characterization of Property (t) in Von Neumann Algebras

We obtain a characterization of property (T) for von Neumann algebras in terms of 1-cohomology similar to the Delorme-Guichardet Theorem for groups.

Relative Hyperbolicity and Bounded Cohomology

Let Γ be a finitely generated group and Γ′ = {Γi | i ∈ I} be a family of its subgroups. We utilize the notion of tuple (Γ,Γ′, X,V ′) that makes the statements and arguments for the pair (Γ,Γ′) parallel to the non-relative case, and define the snake metric dς on the set of edges of a simplicial complex. The language of tuples and snake metrics seems to be convenient for dealing with relative hyp...

Reduced Standard Modules and Cohomology

First cohomology groups of finite groups with nontrivial irreducible coefficients have been useful in several geometric and arithmetic contexts, including Wiles’s famous paper (1995). Internal to group theory, 1-cohomology plays a role in the general theory of maximal subgroups of finite groups, as developed by Aschbacher and Scott (1985).One can pass to the case where the group acts faithfully...