Harmonic cochains and K-theory for ${\tilde{A}}_2$ groups

Abstract

If $\Gamma$ is a torsion free ${\tilde{A}}_2$ group acting on an ${\tilde{A}}_2$ building $\Delta$, and $\fk A_Γ$ is the associated boundary $C^{\ast }$-algebra, it is proved that $K_0(\fk A_Γ)\otimes \bb R \cong \bb R^{2β_2}$, where $β_2=\dim_\bb R H^2(Γ, \bb R)$.

9 Pages

References in corpus (1)

• Boundary operator algebras for free uniform tree lattices