An upper bound on distance degenerate handle additions

2017/07/17 by Yanqing Zou, Zou, Yanqing
Mathematics · #Algebraic Geometry and Number Theory #Ball (mathematics) #Boundary (topology) #Combinatorics #Component (thermodynamics) #Degenerate energy levels #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry #Heegaard splitting #Homotopy and Cohomology in Algebraic Topology #Mathematical analysis #Mathematics #Physics #Pure mathematics #Quantum mechanics #Surface (topology) #Upper and lower bounds #math.GT

paper · pdf · doi:10.48550/arxiv.1707.05053

8figures

arxiv created 2017/07/17 · openalex publication_date 2017/07/17 · arxiv updated 2017/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• 3-Manifolds as viewed from the curve complex
• Horizontal Dehn surgery and genericity in the curve complex
• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds
• Dehn Surgery on Knots

Related

• Degenerating slopes with respect to Heegaard distance
• Proximity in the curve complex: boundary reduction and bicompressible surfaces
• Handle additions producing essential surfaces
• The girth of a Heegaard splitting
• Generalized handlebody sets and non-Haken 3-manifolds