A LINKING NUMBER DEFINITION OF THE AFFINE INDEX POLYNOMIAL AND APPLICATIONS

DOI10.1142/S0218216513410046zbMath1320.57009arXiv1211.1747MaRDI QIDQ2872206

Louis H. Kauffman, Lena C. Folwaczny

Publication date: 14 January 2014

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

Full work available at URL: https://arxiv.org/abs/1211.1747

zbMATH Keywords

virtual knotsmutationsVassiliev invariantsquandlesbiquandles

Mathematics Subject Classification ID

Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) (54H05)

Related Items (23)

The homological arrow polynomial for virtual links ⋮ Alexander and writhe polynomials for virtual knots ⋮ Index polynomials for virtual tangles ⋮ Linking polynomials of virtual string links ⋮ An index definition of parity mappings of a virtual link diagram and Vassiliev invariants of degree one ⋮ Virtual index cocycles and invariants of virtual links ⋮ Twist moves and the affine index polynomials of virtual knots ⋮ The intersection polynomials of a virtual knot II: Connected sums ⋮ Intersection formulas for parities on virtual knots ⋮ The intersection polynomials of a virtual knot I: Definitions and calculations ⋮ A two-variable polynomial invariant of virtual knots ⋮ F-polynomials of tabulated virtual knots ⋮ The writhe and first intersection polynomials of virtual knots of supporting genus one ⋮ Two-variable polynomial invariants of virtual knots arising from flat virtual knot invariants ⋮ Writhe polynomials and shell moves for virtual knots and links ⋮ A homological Casson type invariant of knotoids ⋮ From chord parity to chord index ⋮ Virtual parity Alexander polynomial ⋮ The Wriggle polynomial for virtual tangles ⋮ Some remarks on the chord index ⋮ The multi-variable affine index polynomial ⋮ An unknotting index for virtual links ⋮ The Chord Index, its Definitions, Applications, and Generalizations

Cites Work

• Cosmetic crossings and Seifert matrices
• What is a virtual link?
• On filamentations and virtual knots
• Finite-type invariants of classical and virtual knots
• Concordance and mutation
• Virtual knot theory
• A SEQUENCE OF DEGREE ONE VASSILIEV INVARIANTS FOR VIRTUAL KNOTS
• INTRODUCTION TO VIRTUAL KNOT THEORY
• A NOTE ON NON-CLASSICAL VIRTUAL KNOTS
• A self-linking invariant of virtual knots
• Parity in knot theory

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