Affine three-manifolds with centralizing holonomy

2023/03/29 by Raphaël V Alexandre, Alexandre, Raphaël V
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2303.16665

openalex publication_date 2023/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

According to the Markus conjecture, closed flat affine manifolds with parallel volume should be complete. We show it is the case for three-manifolds when the holonomy centralizes an affine transformation preserving the volume. It is notably the case when the holonomy group has non trivial center or when the automorphism group is non discrete.

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