2024/10/13 by Munro, Zachary, Hoda, Nima
#20F65 #20F67 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.2410.09905
We prove a flat torus theorem for quadric complexes. In particular, we show that if a non-cyclic free abelian group G acts metrically properly on a quadric complex X, then G ≅ ℤ2 and X contains a G-invariant isometric copy of the regular square tiling of the plane. Along the way, we also give a complete proof of the fact that any closed surface subgroup in the fundamental group of a combinatorial 2-complex is represented by a combinatorial map from a cellulation of the surface that is locally injective away from vertices.