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## Harmonic cochains and K-theory for A_2 groups

Lookup NU author(s): Professor Guyan Robertson

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### Abstract

If $\Gamma$ is a torsion free $\widetilde A_2$ group acting on an $\widetilde A_2$ building $\Delta$, and $\fk A_{\Gamma}$ is the associated boundary $C^*$-algebra, it is proved that $K_0(\fk A_\Gamma)\otimes \bb R \cong \bb R^{2\beta_2}$, where $\beta_2=\dim_\bb R H^2(\Gamma, \bb R)$.

Author(s): Robertson G

Publication type: Article

Publication status: In Press

Journal: Groups, Geometry and Dynamics

Year: 2013

ISSN (print): 1661-7207

ISSN (electronic): 1661-7215

Publisher: European Mathematical Society Publishing House