A new class of affine K(π,1) arrangements

2025/11/29 by Goldman, Katherine, Huang, Jingyin
#20F65 (Primary) 20F36 #32S22 #52C35 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2512.00318

Abstract

We show that a certain class of affine hyperplane arrangements are K(π,1) by endowing their Falk complexes with an injective metric. This gives new examples of infinite K(π,1) arrangements in dimension n>2.

Citations

• 353-combinatorial curvature and the 3-dimensional K(π,1) conjecture
• Cycles in spherical Deligne complexes and application to K(π,1)-conjecture for Artin groups
• On spherical Deligne complexes of type D_n
• Labeled four cycles and the K(π,1)-conjecture for Artin groups
• Parabolic subgroups of large-type Artin groups
• The Cartan-Hadamard Theorem for Metric Spaces with Local Geodesic\n Bicombings
• Injective hulls of certain discrete metric spaces and groups
• On the homotopy theory of arrangements, II

Related

• The K(π, 1) conjecture for affine Artin groups
• Topology of plane arrangements and their complements
• Blocking Sets in the complement of hyperplane arrangements in projective space
• Hyperpolygonal arrangements
• Stable hyperplane arrangements