On uniqueness of the equivariant smooth structure on a real moment-angle manifold

2025/03/01 by Nikolai Erokhovets, Erokhovets, Nikolai, Elena Erokhovets +1
Mathematics · #52B05 #52B70 #57R18 #57R91 #57S12 #57S17 #57S25 #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT)

paper · pdf · doi:10.48550/arxiv.2503.00446

openalex publication_date 2025/03/01 · openalex created_date 2025/10/12 · openalex updated_date 2026/07/28

Abstract

The paper is devoted to the well-known problem of smooth structures on moment-angle manifolds. Each real or complex moment-angle manifold has an equivariant smooth structure given by an intersection of quadrics corresponding to a geometric realisation of a polytope. In 2006 F.Bosio and L.Meersseman proved that complex moment-angle manifolds of combinatorially equivalent simple polytopes are equivariantly diffeomorphic. Using arguments from calculus we derive from this result that real moment-angle manifolds of combinatorially equivalent simple polytopes are equivariantly diffeomorphic and the polytopes are diffeomorphic as manifolds with corners.

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