Triangulations of \mathbbRPⁿ with few vertices

2014/03/02 by Soumen Sarkar, Sarkar, Soumen
Computer Science · Mathematics · #52B12 #57Q15 #Advanced Combinatorial Mathematics #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1403.0146

openalex publication_date 2014/03/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

P. Arnoux and A. Marin showed that any triangulation of \mathbbRPⁿ contains more than ((n+1)(n+2))/(2) vertices if n ≥ 3. We construct some natural triangulation of \mathbbRPⁿ with (n(n+5))/(2)-1 vertices for all n ≥ 3. Previously, it was known that \mathbbRPⁿ has ℤ₂ⁿ-equivariant triangulation with n(n+1) vertices for n ≥ 6.

Citations

• Triangulated Manifolds with Few Vertices: Combinatorial Manifolds

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