Topological Lower Bounds on the Sizes of Simplicial Complexes and Simplicial Sets
Abstract
Abstract We prove that if an n -dimensional space X satisfies certain topological conditions then any triangulation of X as well as any its representation as a simplicial set with contractible faces has at least $$2^n$$ 2 n faces of dimension n . One example of such X is the n -dimensional torus $$(S^1)^n$$ ( S 1 ) n .
Fields of Study & Subjects
Advanced Combinatorial Mathematics
Geometric and Algebraic Topology
Topological and Geometric Data Analysis
Publication details
- Journal / source
- Discrete & Computational Geometry
- Volume
- 75
- Issue
- 3
- Pages
- 661–666
- Publication date
- 10 February 2026
- Language
- EN