2009/01/11 by Sangbum Cho, Cho, Sangbum, Darryl McCullough +3 · 1 citation
Mathematics · #57M25 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:57M25
paper · pdf · doi:10.48550/arxiv.0901.1467
8 pages, 4 figures, to appear in Proc. Amer. Math. Soc
arxiv created 2009/01/11 · openalex publication_date 2009/01/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A knot K in 1-bridge position with respect to a genus-g Heegaard surface in a 3-manifold can be moved by isotopy through knots in 1-bridge position until it lies in a union of n parallel genus-g surfaces tubed together by n-1 straight tubes, with K intersecting each tube in two arcs connecting the ends. We prove that the minimum n for which this is possible is equal to a Hempel-type distance invariant defined using an arc complex of the two holed genus-g surface