Pants distances of knotted surfaces in 4-manifolds

2023/07/26 by Román Aranda, Sarah Blackwell, Aranda, Román +11
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2307.13874

openalex publication_date 2023/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define a pants distance for knotted surfaces in 4-manifolds, which generalizes the complexity studied by Blair-Campisi-Taylor-Tomova for surfaces in the 4-sphere. We determine that if the distance computed on a given diagram does not surpass a theoretical bound in terms of the multisection genus, then the pair (X, F) admits a standard form (i.e., has simple topology). Furthermore, we calculate the exact values of our invariants for many new examples, such as the spun lens spaces. We provide a characterization of genus two quadrisections with distance at most six.

Related

• Representing smooth 4-manifolds as loops in the pants complex
• Knotted surfaces in 4-manifolds
• Knotted surfaces in 4-manifolds
• Smoothly knotted and topologically unknotted nullhomologous surfaces in 4-manifolds
• Bounds for Kirby-Thompson invariants of knotted surfaces