Local detection of strongly irreducible Heegaard splittings

DOI10.1016/S0166-8641(97)00184-3zbMath0926.57018OpenAlexW2010371484MaRDI QIDQ1295190

Martin G. Scharlemann

Publication date: 22 November 1999

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0166-8641(97)00184-3

zbMATH Keywords

Heegaard splittingsolid torusstrongly irreducible

Mathematics Subject Classification ID

Related Items (35)

A note on the uniqueness of unstabilized Heegaard splittings of amalgamated 3-manifolds ⋮ The disjoint curve property ⋮ Effective finiteness of irreducible Heegaard splittings of non-Haken 3-manifolds ⋮ Heegaard surfaces and measured laminations. I: the Waldhausen conjecture ⋮ Obtaining genus 2 Heegaard splittings from Dehn surgery ⋮ Heegaard genus and complexity of fibered knots ⋮ Minimal Heegaard genus of amalgamated 3-manifolds ⋮ A sufficient condition for the genus of an amalgamated 3-manifold not to go down ⋮ Short geodesics in hyperbolic 3-manifolds ⋮ The growth rate of the tunnel number of \(m\)-small knots ⋮ Surface bundles with genus two Heegaard splittings ⋮ Some sufficient conditions for tunnel numbers of connected sum of two knots not to go down ⋮ On tunnel numbers of a cable knot and its companion ⋮ Local detection of strongly irreducible Heegaard splittings via knot exteriors. ⋮ The amalgamation of high distance Heegaard splittings along tori ⋮ HEEGAARD GENERA OF ANNULAR 3-MANIFOLDS ⋮ Multiple bridge surfaces restrict knot distance ⋮ Saddle tangencies and the distance of Heegaard splittings ⋮ How a strongly irreducible Heegaard splitting intersects a handlebody ⋮ Rank and genus of 3-manifolds ⋮ The self-amalgamation of high distance Heegaard splittings is always efficient ⋮ An algorithm to determine the Heegaard genus of a 3-manifold ⋮ Sweepouts of amalgamated 3-manifolds ⋮ Heegaard splittings with boundary and almost normal surfaces ⋮ On amalgamations of Heegaard splittings with high distance ⋮ Heegaard surfaces and the distance of amalgamation ⋮ Heegaard splittings of graph manifolds ⋮ A note on Heegaard splittings of amalgamated 3-manifolds ⋮ A lower bound of genus of amalgamations of Heegaard splittings ⋮ Heegaard surfaces and measured laminations, II: Non-Haken 3–manifolds ⋮ Amalgamations of Heegaard splittings in 3-manifolds without some essential surfaces ⋮ Tunnel number one knots, 𝑚-small knots and the Morimoto conjecture ⋮ Locally unknotted spines of Heegaard splittings ⋮ Comparing Heegaard and JSJ structures of orientable 3-manifolds ⋮ Critical Heegaard surfaces

Cites Work

• The topological uniqueness of triply periodic minimal surfaces in \(R^ 3\)
• Reducing Heegaard splittings
• Thin position and Heegaard splittings of the 3-sphere
• Heegaard structures of negatively curved 3-manifolds
• Heegaard-Zerlegungen der 3-Sphäre
• Scindements de Heegaard des espaces lenticulaires
• Unnamed Item
• Unnamed Item

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