1994/04/22 by Donald I. Cartwright, Cartwright, Donald I., Michael Shapiro +1
Mathematics · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals #math.GR
paper · pdf · doi:10.48550/arxiv.math/9404202
Plain Tex, 12 pages, no figures
arxiv created 1994/04/22 · arxiv updated 2009/11/30
We see that a building whose Coxeter group is hyperbolic is itself hyperbolic. Thus any finitely generated group acting co-compactly on such a building is hyperbolic, hence automatic. We turn our attention to affine buildings and consider a group Γ which acts simply transitively and in a ``type-rotating'' way on the vertices of a locally finite thick building of type An. We show that Γ is biautomatic, using a presentation of Γ and unique normal form for each element of Γ, as described in ``Groups acting simply transitively on the vertices of a building of type An'' by D.I. Cartwright, to appear, Proceedings of the 1993 Como conference ``Groups of Lie type and their geometries''.