2009/10/16 by John Berge, Berge, John
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.0910.3038
openalex publication_date 2009/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Embeddings of pairs of disjoint nonparallel primitive simple closed curves in the boundary of a genus two handlebody are classified. Briefly, two disjoint primitives either lie on opposite ends of a product F \boldsymbol× I, or they lie on opposite ends of a kind of "twisted" product F \widetilde\boldsymbol× I, where F is a once-punctured torus. If one of the curves is a proper power of a primitive, the situation is simpler. Either the curves lie on opposite sides of a separating disk in the handlebody, or they bound a nonseparating essential annulus in the handlebody.