2002/10/21 by John Crisp
Mathematics · #Algebra over a field #Algebraic Geometry and Number Theory #Artin group #Cohomological dimension #Cohomology #Combinatorics #Complex dimension #Coxeter group #Dimension (graph theory) #Dimension theory (algebra) #Flag (linear algebra) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical analysis #Mathematics #Piecewise #Pure mathematics #math.GR #math.GT #msc:20F67 #msc:57M20
paper · pdf · doi:10.2140/agt.2002.2.921
published as Algebr. Geom. Topol. 2 (2002) 921-936 · Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-37.abs.html
openalex publication_date 2002/10/21 · arxiv created 2002/11/07 · arxiv updated 2014/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Let K be a 2-dimensional finite flag complex. We study the CAT(0) dimension of the 'Bestvina-Brady group', or 'Artin kernel', K . We show that K has CAT(0) dimension 3 unless K admits a piecewise Euclidean metric of non-positive curvature. We give an example to show that this implication cannot be reversed. Different choices of K lead to examples where the CAT(0) dimension is 3, and either (i) the geometric dimension is 2, or (ii) the cohomological dimension is 2 and the geometric dimension is not known.