Multiple bridge surfaces restrict knot distance

DOI10.2140/agt.2007.7.957zbMath1142.57005arXivmath/0511139OpenAlexW2119010810MaRDI QIDQ2464778

Maggy Tomova

Publication date: 17 December 2007

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

Full work available at URL: https://arxiv.org/abs/math/0511139

zbMATH Keywords

Heegaard splittingbridge surfacebridge positionknot distance

Mathematics Subject Classification ID

Related Items (23)

Distance two links ⋮ High distance bridge surfaces ⋮ Neighbors of Knots in the Gordian Graph ⋮ Double branched covers of tunnel number one knots ⋮ Topological quantum computation is hyperbolic ⋮ Independence of volume and genus 𝑔 bridge numbers ⋮ Bridge splittings of links with distance exactly \(n\) ⋮ Links, bridge number, and width trees ⋮ Width is not additive ⋮ Flipping bridge surfaces and bounds on the stable bridge number ⋮ Bridge spectra of cables of 2-bridge knots ⋮ Bridge decompositions with distances at least two ⋮ High distance knots ⋮ Exceptional and cosmetic surgeries on knots ⋮ Knots and surfaces ⋮ Meridional almost normal surfaces in knot complements ⋮ Conway products and links with multiple bridge surfaces ⋮ Rectangle condition for bridge decompositions of links ⋮ Properties of Casson–Gordon’s rectangle condition ⋮ Distance and the Goeritz groups of bridge decompositions ⋮ A locally minimal, but not globally minimal, bridge position of a knot ⋮ Essential surfaces in highly twisted link complements ⋮ Knots with compressible thin levels

Cites Work

• Heegaard splittings of Haken manifolds have bounded distance.
• Distance and bridge position
• Proximity in the curve complex: boundary reduction and bicompressible surfaces
• Reducing Heegaard splittings
• Local detection of strongly irreducible Heegaard splittings
• Annuli in generalized Heegaard splittings and degeneration of tunnel number
• Comparing Heegaard splittings of non-Haken 3-manifolds
• Alternate Heegaard genus bounds distance
• Uniqueness of bridge surfaces for 2-bridge knots
• Thinning Genus Two Heegaard Spines in S³
• Thin position for knots in a 3-manifold
• 3-manifolds as viewed from the curve complex

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