2002/06/09 by Tsuyoshi Kobayashi, Kobayashi, Tsuyoshi, Yo'av Rieck +1
Mathematics · #57M99 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:57M99
paper · pdf · doi:10.48550/arxiv.math/0206085
12 pages
arxiv created 2002/06/09 · arxiv updated 2009/11/30
We study the way a strongly irreducible Heegaard surface Σ intersects a knot exterior X embedded in a 3-manifold, and show that if Σ∩ ∂ X consists of simple closed curves which are essential in both Σ and ∂ X, then the intersection X ∩ Σ consists of meridional annuli only. As an application we show that when considering two Heegaard surfaces that intersect essentially and spinally (cf. Rubinstein and Shcarlemann) any embedded torus in the union of the two bounds a solid torus.