JournalsggdVol. 8, No. 1pp. 245–255

Harmonic cochains and K-theory for A~2\tilde{A}_2-groups

  • Guyan Robertson

    University of Newcastle, Newcastle upon Tyne, Great Britain
Harmonic cochains and K-theory for $\tilde{A}_2$-groups cover
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Abstract

If Γ\Gamma is a torsion free A~2\tilde{A}_2-group acting on an A~2\tilde{A}_2 building Δ\Delta, and AΓ\mathfrak{A}_{\Gamma} is the associated boundary CC^*-algebra, it is proved that K0(AΓ)RR2β2K_0(\mathfrak{A}_\Gamma)\otimes \mathbb{R} \cong \mathbb{R}^{2\beta_2}, where β2=dimRH2(Γ,R)\beta_2=\dim_{\mathbb{R}} H^2(\Gamma, \mathbb{R}).

Cite this article

Guyan Robertson, Harmonic cochains and K-theory for A~2\tilde{A}_2-groups. Groups Geom. Dyn. 8 (2014), no. 1, pp. 245–255

DOI 10.4171/GGD/224