2025/10/07 by Daryl Cooper, Cooper, Daryl, Leslie Mavrakis +3
Computer Science · Mathematics · #57Q99 #Advanced Combinatorial Mathematics #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Graph Labeling and Dimension Problems
paper · pdf · doi:10.48550/arxiv.2510.06514
openalex publication_date 2025/10/07 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28
A family of compact n-manifolds is locally combinatorially defined (LCD) if it can be specified by a finite number of local triangulations. We show that LCD is equivalent to the existence of a compact branched n-manifold W, such that the family is precisely those manifolds that immerse into W. In subsequent papers, the equivalence will be used to show that, for each of the eight Thurston geometries, the family of closed 3-manifolds admitting that geometry is LCD.