Unknotting number, genus and companion tori

DOI10.1007/BF01456051zbMath0616.57003MaRDI QIDQ1821388

Martin G. Scharlemann, Abigail A. Thompson

Publication date: 1988

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/164360

zbMATH Keywords

incompressible toruswinding numberunknotting numbersatellite knotsutured manifoldgenus of a knotcrossing linkcrossing changescompanion toricrossing disk

Mathematics Subject Classification ID

Related Items (20)

Concordance of decompositions given by defining sequences ⋮ Genera, band sum of knots and Vassiliev invariants ⋮ Unknotting Number One Knots are Prime: A New Proof ⋮ Knots with unknotting number 1 and essential Conway spheres ⋮ 4-Move distance of knots ⋮ Knot adjacency and fibering ⋮ Satellite knots and trivializing bands ⋮ A characterization of the Γ-polynomials of knots with clasp number at most two ⋮ Knot adjacency and satellites. ⋮ Raising crosscap number while lowering unknotting number ⋮ Only single twists on unknots can produce composite knots ⋮ Primeness of Twisted Knots ⋮ Comparing 2-handle additions to a genus 2 boundary component ⋮ An infinite family of prime knots with a certain property for the clasp number ⋮ Crossing changes ⋮ Geometric indices and the Alexander polynomial of a knot ⋮ Chirurgies de Dehn de pente \(\pm 1\) sur certains noeds dans les 3- variétés. (Dehn surgery of genus \(\pm 1\) on certain knots in 3- manifolds) ⋮ UNKNOTTING NUMBER AND GENUS OF 3-BRAID KNOTS ⋮ Generalized Unknotting Operations and Tangle Decompositions ⋮ Lernaean knots and band surgery

Cites Work

• Unknotting number one knots are prime
• Genus is superadditive under band connected sum
• Foliations and the topology of 3-manifolds. II
• Property P for the band-connect sum of two knots
• Sutured manifolds and generalized Thurston norms
• Smooth spheres in \({\mathbb{R}}^ 4\) with four critical points are standard
• Only integral Dehn surgeries can yield reducible manifolds
• Simple Knots in Compact, Orientable 3-Manifolds
• Simple Knots Without Unique Minimal Surfaces

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