Minimal Simplicial Spherical Mappings with a Given Degree
Abstract
We study the minimal number $$\lambda(n,d)$$ of vertices of a triangulation of the $$n$$ -sphere to admit a simplicial map to the boundary of an $$(n+1)$$ -simplex with a given degree $$d$$ . For each dimension $$n$$ , we find upper estimates for $$\lambda(n,d)$$ and obtain the asymptotics of this number with increasing degree. For small degrees ( $$d=2,3,4$$ ), we show that the minimal number of vertices is $$n+d+3$$ . A key technical result is an identity that reduces higher-dimensional cases to lower-dimensional ones.
Fields of Study & Subjects
Computational Geometry and Mesh Generation
Digital Image Processing Techniques
Geometric and Algebraic Topology
Publication details
- Journal / source
- Mathematical Notes
- Publisher
- Pleiades Publishing Ltd
- Volume
- 119
- Issue
- 5-6
- Pages
- 1021–1024
- Publication date
- 1 May 2026
- Language
- EN