2009/10/29 by Rena Levitt, Jon McCammond, Levitt, Rena +1
Computer Science · Mathematics · #20F65 #20F67 #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematics and Applications #math.GR #msc:20F65 #msc:20F67
paper · pdf · doi:10.48550/arxiv.0910.5688
34 pages, 12 figures
arxiv created 2009/10/29 · openalex publication_date 2009/10/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the early 1990s Steve Gersten and Hamish Short proved that compact nonpositively curved triangle complexes have biautomatic fundamental groups and that compact nonpositively curved square complexes have biautomatic fundamental groups. In this article we report on the extent to which results such as these extend to nonpositively curved complexes built out a mixture of triangles and squares. Since both results by Gersten and Short have been generalized to higher dimensions, this can be viewed as a first step towards unifying Januszkiewicz and Świȧtkowski's theory of simplicial nonpositive curvature with the theory of nonpositively curved cube complexes.