The topological holonomy group and the complexity of horizontality

2024/07/14 by Naoya Ando, Yonezaki, Anri, Ando, Naoya
Computer Science · Mathematics · #Differential Geometry (math.DG) #Digital Image Processing Techniques #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2407.10092

openalex publication_date 2024/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Based on [1], we study the complexity of horizontality in each twistor space E_ε associated with an oriented vector bundle E of rank 4 with a positive-definite metric over the 2-torus T², and obtain classification of the topological holonomy groups in SO(3). We observe that there exist many topological holonomy groups in SO(3) generated by two finite order elements and equipped with noncommutative pairs which consist of infinite order elements. We find topological holonomy groups which are dense in SO(4).

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