Triangulations of Grassmannians and flag manifolds

2022/05/19 by Olakunle S. Abawonse, Abawonse, Olakunle S
Computer Science · Mathematics · #57-08 (primary) 14P25 (secondary) 52C40 (secondary) #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2205.09553

openalex publication_date 2022/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

MacPherson conjectured that the Grassmannian Gr(2, ℝⁿ) has the same homeomorphism type as the combinatorial Grassmannian ‖MacP(2,n)‖, while Babson proved that the spaces Gr(2,ℝⁿ) and Gr(1,2,ℝⁿ) are homotopy equivalent to their combinatorial analogs ‖MacP(2,n)‖ and ‖MacP(1,2,n)‖ respectively. We will prove that Gr(2, ℝⁿ) and Gr(1,2, ℝⁿ) are homeomorphic to ‖MacP(2,n)‖ and ‖MacP(1,2,n)‖ respectively.

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