2008/06/09 by Frédéric Meunier, Meunier, Frédéric
Computer Science · Mathematics · #37F20 #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.AT #math.CO #msc:37F20
paper · pdf · doi:10.48550/arxiv.0806.1488
Presented at the TGGT 08 Conference, May 2008, Paris. The definition of a polytopal map has been modified
openalex publication_date 2008/06/09 · arxiv created 2008/07/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The notion of polytopal map between two polytopal complexes is defined. Surprisingly, this definition is quite simple and extends naturally those of simplicial and cubical maps. It is then possible to define an induced chain map between the associated chain complexes. Finally, we use this new tool to give the first combinatorial proof of the splitting necklace theorem of Alon. The paper ends with open questions, such as the existence of Sperner's lemma for a polytopal complex or the existence of a cubical approximation theorem.