2024/07/08 by Suhyoung Choi, Choi, Suhyoung
Mathematics · Physics and Astronomy · #57M50 #83A99 #Advanced Differential Geometry Research #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2407.05932
openalex publication_date 2024/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let E be a flat Lorentzian space of signature (2, 1). A Margulis space-time is a noncompact complete Lorentz flat 3-manifold E/Γ with a free isometry group Γ of rank g ≥ 2. We consider the case when Γ contains a parabolic element. We show that sufficiently small deformations of Γ still act properly on E. We use our previous work showing that E/Γ can be compactified relative to a union of solid tori and some old idea of Carrière in his famous work. We will show that the there is also a decomposition of E/Γ by crooked planes that are disjoint and embedded in a generalized sense. These can be perturbed so that E/Γ decomposes into cells. This partially affirms the conjecture of Charette-Drumm-Goldman.