Triangles, squares and geodesics. (Q2909487)

Several classes of CAT(0) groups are known to be biautomatic, and the first result in this direction is probably the one of \textit{S. M. Gersten} and \textit{H. B. Short} [Invent. Math. 102, No. 2, 305-334 (1990; Zbl 0714.20016)] stating that the fundamental group of any compact nonpositively curved triangle (respectively square) complex is biautomatic.NEWLINENEWLINE The authors in the paper under review conjecture that the result extends to nonpositively curved complexes made out of a mixture of triangles and squares. They establish a partial result in this direction, namely, that for every compact nonpositively curved triangle-square complex \(K\) there exists a canonically defined language of geodesics that reduces to the regular languages used by Short and Gersten in the case where \(K\) is a triangle or a square complex.