On sections of configurations of points on orientable surfaces

2024/11/25 by Stavroula Makri, Makri, Stavroula · 1 citation
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #FOS: Mathematics #Geometric Topology (math.GT) #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2411.16409

openalex publication_date 2024/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the configuration space of distinct, unordered points on compact orientable surfaces of genus g, denoted S_g. Specifically, we address the section problem, which concerns the addition of n distinct points to an existing configuration of m distinct points on S_g in a way that ensures the new points vary continuously with respect to the initial configuration. This problem is equivalent to the splitting problem in surface braid groups. With an algebraic approach, for g≥ 1 and m≥ 2, we establish a necessary condition for the existence of a section, showing that if a section exists, then n must be a multiple of m+(2g-2). For g≥ 1 and m=1, we take a geometric approach to demonstrate that a section exists for all values of n.

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