Groups, Geometry, and Dynamics

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Volume 8, Issue 1, 2014, pp. 245–255
DOI: 10.4171/GGD/224

Published online: 2014-05-13

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

Guyan Robertson[1]

(1) University of Newcastle, Newcastle upon Tyne, Great Britain

If $\Gamma$ is a torsion free $\tilde{A}_2$-group acting on an $\tilde{A}_2$ building $\Delta$, and $\mathfrak{A}_{\Gamma}$ is the associated boundary $C^*$-algebra, it is proved that $K_0(\mathfrak{A}_\Gamma)\otimes \mathbb{R} \cong \mathbb{R}^{2\beta_2}$, where $\beta_2=\dim_{\mathbb{R}} H^2(\Gamma, \mathbb{R})$.

Keywords: Euclidean building, boundary, operator algebra

Robertson Guyan: Harmonic cochains and K-theory for $\tilde{A}_2$-groups. Groups Geom. Dyn. 8 (2014), 245-255. doi: 10.4171/GGD/224