Folding median graphs
arXiv:2311.09751
Abstract
Extending Stallings' foldings of trees, we show in this article that every parallel-preserving map between median graphs factors as an isometric embedding through a sequence of elementary transformations which we call foldings and swellings. This new construction proposes a unified point of view on Beeker and Lazarovich's work on folding pocsets and on Ben-Zvi, Kropholler, and Lyman's work on folding nonpositively curved cube complexes.
arXiv comment45 pages, 5 figures. Comments are welcome!