2025/02/01 by Giovanni Bellettini, Bellettini, Giovanni, Maurizio Paolini +3
Engineering · Mathematics · Computer Science · #Human Motion and Animation #Geometric and Algebraic Topology #Artificial Intelligence in Games
paper · pdf · doi:10.48550/arxiv.2502.00422
The paper considers the uniqueness question of factorization of a knotted handlebody in the 3-sphere along decomposing 2-spheres. We obtain a uniqueness result for factorization along decomposing 2-spheres meeting the handlebody at three parallel disks. The result is used to examine handlebody-knot symmetry; particularly, the chirality of 610 in the handlebody-knot table, previously unknown, is determined. In addition, an infinite family of hyperbolic handlebody-knots with homeomorphic exteriors is constructed.