2001/07/01 by Jacek Świątkowski · 1 citation
Mathematics · #Advanced Topics in Algebra #Finite Group Theory Research #Geometric and Algebraic Topology #Automorphism #Transitive relation #Class (philosophy) #Mathematics #Construct (python library) #Group (periodic table) #Automorphism group #Combinatorics #Pure mathematics #Computer science #Artificial intelligence #Physics
paper · doi:10.1093/qjmath/52.2.231
openalex publication_date 2001/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
In this paper we construct a class of groups together with their actions on certain spaces called polygonal complexes. We give a complete description of the class of all groups which act by automorphisms simply transitively on the oriented edges of non‐positively curved polygonal complexes. This family of group actions is very natural from a geometrical viewpoint, being a kind of higher‐dimensional analogue of the actions of groups on their Cayley graphs (which are simply transitive on vertices). The construction is based on the notion of a non‐positively curved orbihedron and its fundamental group and generalizes the ideas of Ballmann and the author [2].