2025/06/18 by Jumpei Yasuda, Yasuda, Jumpei
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2506.15401
openalex publication_date 2025/06/18 · openalex created_date 2025/10/19 · openalex updated_date 2026/07/28
An n-plat 1-knot is one isotopic to the plat closure of some 2n-braid, which is also called an n-bridge 1-knot. Schubert classified 2-bridge 1-knots by considering their double branched covers which are homeomorphic to lens spaces. A 2-knot is a 2-sphere smoothly embedded in 4-space or 4-sphere. An n-plat 2-knot is one isotopic to the plat closure of some 2-dimensional 2n-braid. The aim of this paper is to classify 2-plat 2-knots. By a result of Montesinos, double branched covers do not distinguish 2-plat 2-knots. Thus, we introduce a new invariant to classify them. Our invariant serves as an analogue of a torsion invariant. Furthermore, it is an obstruction to invertibility of 2-knots.