Systolizing buildings

2013/10/21 by Piotr Przytycki, Petra Schwer, Przytycki, Piotr +1
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #math.CO #math.GR #math.GT

paper · pdf · doi:10.48550/arxiv.1310.5525

29 pages, 14 figures

arxiv created 2014/06/30 · arxiv updated 2014/07/01

Abstract

We introduce a construction turning some Coxeter and Davis realizations of buildings into systolic complexes. Consequently groups acting geometrically on buildings of triangle types distinct from (2,4,4), (2,4,5), (2,5,5), and various rank 4 types are systolic.

Related

• The triangle groups (2,4,5) and (2,5,5) are not systolic
• The (2,4,5) triangle Coxeter group is not systolic
• A combinatorial non-positive curvature I: weak systolicity
• Lattices in hyperbolic buildings
• A construction of lattices for certain hyperbolic buildings