Homotopy equivalence of Grassmannians and MacPhersonians in rank 3

2025/04/01 by Dobbins, Michael Gene
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2504.01180

Abstract

We confirm a long standing conjecture in the case of rank 3 that MacPhersonians are homotopy equivalent to Grassmannians.

Related

• On The Acyclic MacPhersonian
• Triangulations of Grassmannians and flag manifolds
• Grassmannians over a finite field
• Grassmannians and representations
• On D.K. Biss' papers "The homotopy type of the matroid Grassmannian" and "Oriented matroids, complex manifolds, and a combinatorial model for BU"