Year: 2024
Type: preprint
Abstract: 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 $G \cong \mathbb{Z}^2$ 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.
Source: arXiv (Cornell University)
Authors: Hoda, Nima, Munro, Zachary
Institutions: Cornell University, McGill University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4403570214