Twisted link theory

DOI10.2140/agt.2008.8.1249zbMath1149.57004arXivmath/0608233OpenAlexW2083589095MaRDI QIDQ945658

Mario O. Bourgoin

Publication date: 17 September 2008

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

Full work available at URL: https://arxiv.org/abs/math/0608233

zbMATH Keywords

fundamental groupJones polynomialvirtual linkstable equivalenceprojective link

Mathematics Subject Classification ID

Relations of low-dimensional topology with graph theory (57M15) Fundamental group, presentations, free differential calculus (57M05)

Related Items (22)

Unknotting twisted knots with Gauss diagram forbidden moves ⋮ One conjecture on cut points of virtual links and the arrow polynomial of twisted links ⋮ On Twisted Knots ⋮ VIRTUAL SHADOW MODULES AND THEIR LINK INVARIANTS ⋮ Twisted virtual bikeigebras and twisted virtual handlebody-knots ⋮ Converting virtual link diagrams to normal ones ⋮ A table of twisted knots with crossing number 3 ⋮ Polynomial invariants and quandles of twisted links ⋮ Surface pole bracket polynomials of virtual knots and twisted knots ⋮ A twisted link invariant derived from a virtual link invariant ⋮ Twisted intersection colorings, invariants and double coverings of twisted links ⋮ Khovanov homology, Lee homology and a Rasmussen invariant for virtual knots ⋮ Parity in knot theory and graph-links ⋮ Generalizations of the Kauffman polynomial for knotsin the thickened surface of genus 2 ⋮ BIQUANDLES WITH STRUCTURES RELATED TO VIRTUAL LINKS AND TWISTED LINKS ⋮ Additional gradings in the Khovanov complex for thickened surfaces ⋮ INDEX POLYNOMIAL INVARIANTS OF TWISTED LINKS ⋮ Virtual links which are equivalent as twisted links ⋮ Turaev hyperbolicity of classical and virtual knots ⋮ Group presentations for links in thickened surfaces ⋮ The polynomial invariants of twisted links ⋮ The Chord Index, its Definitions, Applications, and Generalizations

Cites Work

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• Curves on surfaces virtual knots, and the Jones-Kaufmann polynomial
• State models and the Jones polynomial
• What is a virtual link?
• Virtual knot theory
• On combinatorial isotopy
• A polynomial invariant for knots via von Neumann algebras
• Diagrammatic Unknotting of Knots and Links in the Projective Space
• UNKNOTTING VIRTUAL KNOTS WITH GAUSS DIAGRAM FORBIDDEN MOVES
• ABSTRACT LINK DIAGRAMS AND VIRTUAL KNOTS
• Polynomial invariants of links in the projective space

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