Rectangle condition for compression body and 2-fold branched covering

2010/07/15 by Jungsoo Kim, Jung Hoon Lee, Kim, Jungsoo +1 · 1 citation
Engineering · Materials Science · Mathematics · #57M25 #57M50 #Elasticity and Material Modeling #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #High-Velocity Impact and Material Behavior #math.GT #msc:57M25 #msc:57M50

paper · pdf · doi:10.48550/arxiv.1007.2521

16 pages, 15 figures

arxiv created 2010/07/15 · openalex publication_date 2010/07/15 · arxiv updated 2010/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give the rectangle condition for strong irreducibility of Heegaard splittings of 3-manifolds with non-empty boundary. We apply this to a generalized Heegaard splitting of a 2-fold covering of S³ branched along a link. The condition implies that any thin meridional level surface in the link complement is incompressible. We also show that the additivity of knot width holds for a composite knot satisfying the condition.

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