On keen weakly reducible bridge spheres

DOI10.2140/AGT.2024.24.4201MaRDI QIDQ6660971

Puttipong Pongtanapaisan, Daniel Rodman

Publication date: 10 January 2025

Published in: Algebraic \& Geometric Topology (Search for Journal in Brave)

zbMATH Keywords

curve complexBachman's topological indexbridge positions

Mathematics Subject Classification ID

2-dimensional topology (including mapping class groups of surfaces, Teichmüller theory, curve complexes, etc.) (57K20) Knot theory (57K10) General topology of 3-manifolds (57K30)

Cites Work

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• Bridge spheres for the unknot are topologically minimal
• Properties of knots preserved by cabling
• Topologically minimal surfaces versus self-amalgamated Heegaard surfaces
• An infinite family of links with critical bridge spheres
• Hyperbolic manifolds containing high topological index surfaces
• Bridge distance and plat projections
• Width complexes for knots and 3-manifolds
• Topological index theory for surfaces in 3-manifolds
• Least area incompressible surfaces in 3-manifolds
• Reducible handle additions to weakly reducible Heegaard splittings
• Stabilizing and destabilizing Heegaard splittings of sufficiently complicated 3-manifolds
• On the existence of high index topologically minimal surfaces
• On keen weakly reducible Heegaard splittings
• A topologically minimal, weakly reducible, unstabilized Heegaard splitting of genus three is critical
• Virtually geometrically finite mapping class groups of 3-manifolds
• Minimal Surfaces with Low Index in the Three-Dimensional Sphere
• Nonminimal bridge positions of torus knots are stabilized
• The disk complex and topologically minimal surfaces in the 3-sphere
• On topologically minimal surfaces of high genus
• Homeomorphisms of the 3-sphere that preserve a Heegaard splitting of genus two

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