Small examples of non-constructible simplicial balls and spheres

2003/09/08 by Frank H. Lutz, Lutz, Frank H.
Computer Science · Mathematics · #52B05 #52B22 #57M25 #57Q15 #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Point processes and geometric inequalities #math.CO #math.GT #msc:52B05 #msc:52B22 #msc:57M25 #msc:57Q15

paper · pdf · doi:10.48550/arxiv.math/0309149

9 pages, 3 figures

arxiv created 2003/09/08 · openalex publication_date 2003/09/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct non-constructible simplicial d-spheres with d+10 vertices and non-constructible, non-realizable simplicial d-balls with d+9 vertices for d≥ 3.

Citations

• Shrinking Cell-Like Decompositions of Manifolds. Codimension Three

Related

• Deciding nonconstructibility of 3-balls with strict spanning edges
• Parsimonious cones
• The non-pure version of the simplex and the boundary of the simplex
• A non-face characterization of spheres on few vertices
• Constructions of d-spheres from (d-1)-spheres and d-balls with same set of vertices