Hyperbolic small knots in spherical manifolds

2025/06/01 by Ichihara, Kazuhiro
#FOS: Mathematics #Geometric Topology (math.GT) #Primary 57K10 #Secondary 57K32

paper · doi:10.48550/arxiv.2506.01041

Abstract

It was conjectured by Lopez that every closed irreducible non-Haken 3-manifold contains a small knot. In this paper, we give explicit examples of hyperbolic small knots in most closed orientable spherical 3-manifolds other than prism manifolds.

Citations

• Small knots of large Heegaard genus
• Exceptional Dehn surgery on the minimally twisted five-chain link
• Exceptional surgeries on components of two-bridge links
• Counting genus one fibered knots in lens spaces
• Computing boundary slopes of 2-bridge links
• The entropy formula for the Ricci flow and its geometric applications
• The Geometries of 3-Manifolds

Related

• Hyperbolic Knots
• Small curvature surfaces in hyperbolic 3-manifolds
• Exceptional surgeries in 3-manifolds
• Some 4-manifold geometry from hyperbolic knots in S³
• Hyperbolic Knot Theory