An upper bound on distance degenerate handle additions

Abstract

We prove that for any distance at least 3 Heegaard splitting and a boundary component $F$, there is a diameter finite ball in the curve complex $\mathcal{C}(F)$ so that it contains all distance degenerate curves or slopes in $F$.

arXiv comment8figures

References in corpus (6)

• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds
• Alternate Heegaard genus bounds distance
• High distance knots
• Heegaard splittings of distance exactly $n$
• Horizontal Dehn Surgery and genericity in the curve complex
• Degenerating slopes with respect to Heegaard distance