Alternating knots with unknotting number one

DOI10.1016/j.aim.2016.09.033zbMath1353.57013arXiv1312.1278OpenAlexW2963087536MaRDI QIDQ340422

Duncan McCoy

Publication date: 14 November 2016

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.1278

zbMATH Keywords

Dehn surgeryalternating knotunknotting numberbranched double coverchangemaker latticeGoeritz matrixMontesinos trick

Mathematics Subject Classification ID

Lattices and convex bodies in (n) dimensions (aspects of discrete geometry) (52C07) Relations of low-dimensional topology with graph theory (57M15) Low-dimensional topology of special (e.g., branched) coverings (57M12)

Related Items

Non-integer surgery and branched double covers of alternating knots ⋮ Untwisting information from Heegaard Floer homology ⋮ Bounds on alternating surgery slopes ⋮ Links with splitting number one ⋮ A Counterexample to the Bernhard–Jablan Unknotting Conjecture ⋮ Genera of knots in the complex projective plane

Uses Software

• KnotInfo

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Pretzel knots with unknotting number one
• Cosmetic surgeries on knots in \(S^3\)
• Knots with unknotting number one and Heegaard Floer homology
• On the Heegaard Floer homology of branched double-covers
• Khovanov homology and the slice genus
• Knot Floer homology and rational surgeries
• The classification of alternating links
• Knots with unknotting number 1 and essential Conway spheres
• A remark on Khovanov homology and two-fold branched covers
• State models and the Jones polynomial
• Kauffman's polynomial and alternating links
• Homology of group systems with applications to knot theory
• Genus of alternating link types
• On the signature of a link
• On Culler-Shalen seminorms and Dehn filling
• Gauge theory for embedded surfaces. I
• On the Floer homology of plumbed three-manifolds
• Polynomial values, the linking form and unknotting numbers
• An application of gauge theory to four dimensional topology
• Knots.
• The lens space realization problem
• L-space surgeries, genus bounds, and the cabling conjecture
• Donaldson's theorem, Heegaard Floer homology, and knots with unknotting number one
• Unknotting information from Heegaard Floer homology
• Some Examples Related to 4-Genera, Unknotting Numbers and Knot Polynomials
• Non-integer surgery and branched double covers of alternating knots
• A note on unknotting number
• Two-Bridge Links with Unlinking Number One
• Deficiency Symmetries of Surgeries in S3
• The almost alternating diagrams of the trivial knot
• Jones Polynomials of Alternating Links
• Unknotting Information from 4-Manifolds
• UNKNOTTING NUMBERS AND MINIMAL KNOT DIAGRAMS
• Two-Bridge Knots with Unknotting Number One
• On a Certain Numerical Invariant of Link Types
• Note on Complete Sequences of Integers
• Dehn surgery on knots