The efficient certification of knottedness and Thurston norm

DOI10.1016/j.aim.2021.107796OpenAlexW3172337659MaRDI QIDQ2037601

Marc Lackenby

Publication date: 8 July 2021

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

Full work available at URL: https://arxiv.org/abs/1604.00290

zbMATH Keywords

genusThurston normNPunknot recognitionco-NPsutured manifold hierarchy

Mathematics Subject Classification ID

Theory of computing (68Qxx) Differential topology (57Rxx) PL-topology (57Qxx) Knot theory (57K10)

Related Items

A Survey of the Thurston Norm, Some conditionally hard problems on links and 3-manifolds, On dual unit balls of Thurston norms, Finding non-orientable surfaces in 3-manifolds, The computational complexity of knot genus in a fixed 3‐manifold, Algorithms for contractibility of compressed curves on 3-manifold boundaries, The computational complexity of classical knot recognition, On meridian-traceless \(\mathrm{SU}(2)\)-representations of link groups, Pole dancing: 3D morphs for tree drawings, Morphing tree drawings in a small 3D grid, Shellings from relative shellings, with an application to NP-completeness, Unnamed Item, Pole Dancing: 3D Morphs for Tree Drawings, On the complexity of torus knot recognition, Frontiers of sphere recognition in practice

Cites Work

• Theorie der Normalflächen. Ein Isotopiekriterium für den Kreisknoten
• An algorithm to decide if a 3-manifold is a Haken manifold
• Triangulations of fibre-free Haken 3-manifolds
• Foliations and genera of links
• Sutured manifolds and generalized Thurston norms
• Homotopy equivalences of 3-manifolds with boundaries
• Essential laminations and Kneser normal form
• The size of triangulations supporting a given link
• The size of spanning disks for polygonal curves
• Decision problems in the space of Dehn fillings
• Exceptional surgery curves in triangulated 3-manifolds.
• Algorithms for the complete decomposition of a closed \(3\)-manifold
• Taut normal surfaces
• Knottedness is in NP, modulo GRH
• The computational complexity of basic decision problems in 3-dimensional topology
• On irreducible 3-manifolds which are sufficiently large
• The number of Reidemeister moves needed for unknotting
• The computational complexity of knot and link problems
• Seifert fibered spaces in irreducible, sufficiently-large 3-manifolds
• Dehn surgery on knots in 3-manifolds
• The computational complexity of knot genus and spanning area
• Foliations and the topology of 3-manifolds
• Algorithmic topology and classification of 3-manifolds
• Computational Complexity
• Unnamed Item
• Unnamed Item
• Unnamed Item