Alexander invariants for virtual knots

DOI10.1142/S0218216515500091zbMath1364.57005arXiv1409.1459MaRDI QIDQ5255347

Emily Dies, Hans U. Boden, Eric Harper, Adam Gerlings, Anne Isabel Gaudreau, Andrew J. Nicas

Publication date: 15 June 2015

Published in: Journal of Knot Theory and Its Ramifications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.1459

zbMATH Keywords

virtual knotstwisted Alexander polynomialsknot groupsvirtual crossing numberAlexander invariants of virtual knots

Mathematics Subject Classification ID

Related Items (21)

On ribbon graphs and virtual links ⋮ Virtual and universal braid groups, their quotients and representations ⋮ Alexander and writhe polynomials for virtual knots ⋮ Multi-switches and virtual knot invariants ⋮ Peripheral elements in reduced Alexander modules ⋮ Multi-switches and representations of braid groups ⋮ Representations of flat virtual braids which do not preserve the forbidden relations ⋮ Representations of virtual braids by automorphisms and virtual knot groups ⋮ Multi-switches, representations of virtual braids, and invariants of virtual links ⋮ On the lower central series of some virtual knot groups ⋮ Virtual knot groups and almost classical knots ⋮ Groups of the virtual trefoil and Kishino knots ⋮ From chord parity to chord index ⋮ Virtual parity Alexander polynomial ⋮ Virtual Knot Cobordism and Bounding the Slice Genus ⋮ Burau Maps and Twisted Alexander Polynomials ⋮ Virtually symmetric representations and marked Gauss diagrams ⋮ On the new representation of the virtual braid group ⋮ Virtual concordance and the generalized Alexander polynomial ⋮ Milnor's concordance invariants for knots on surfaces ⋮ Some congruence of the generalized Alexander invariant for periodic virtual links

Cites Work

• Metabelian representations, twisted Alexander polynomials, knot slicing, and mutation
• Twisted Alexander polynomials detect fibered 3-manifolds
• Twisted Alexander polynomials detect the unknot
• Twisted Alexander invariants, Reidemeister torsion, and Casson-Gordon invariants
• Twisted Alexander polynomial for finitely presentable groups
• What is a virtual link?
• Finite-type invariants of classical and virtual knots
• On invariants of virtual links
• Virtual knot theory
• Twisted Alexander polynomials of periodic knots
• Twisted Alexander polynomials and surjectivity of a group homomorphism
• Lower Bounds on Virtual Crossing Number and Minimal Surface Genus
• Virtual knot theory–-unsolved problems
• A Partial Order in the Knot Table
• CROWELL'S DERIVED GROUP AND TWISTED POLYNOMIALS
• Criteria for virtual fibering
• QUATERNIONIC INVARIANTS OF VIRTUAL KNOTS AND LINKS
• VIRTUAL CROSSING NUMBER AND THE ARROW POLYNOMIAL
• POLYNOMIAL INVARIANTS OF VIRTUAL LINKS
• FORBIDDEN MOVES UNKNOT A VIRTUAL KNOT
• ALEXANDER GROUPS AND VIRTUAL LINKS
• UNKNOTTING VIRTUAL KNOTS WITH GAUSS DIAGRAM FORBIDDEN MOVES
• ABSTRACT LINK DIAGRAMS AND VIRTUAL KNOTS
• VIRTUAL KNOT PRESENTATION OF RIBBON TORUS-KNOTS
• VIRTUAL KNOT GROUPS AND THEIR PERIPHERAL STRUCTURE
• A NOTE ON NON-CLASSICAL VIRTUAL KNOTS
• POLYNOMIAL KNOT AND LINK INVARIANTS FROM THE VIRTUAL BIQUANDLE
• A PARTIAL ORDER ON THE SET OF PRIME KNOTS WITH UP TO 11 CROSSINGS
• Groups of virtual and welded links
• Representations of knot groups and twisted Alexander polynomials

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