Parity in knot theory and graph-links
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Publication:459460
DOI10.1007/s10958-013-1499-yzbMath1320.57001OpenAlexW2021325128MaRDI QIDQ459460
I. M. Nikonov, D. P. Il'yutko, Vassily O. Manturov
Publication date: 13 October 2014
Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10958-013-1499-y
Relations of low-dimensional topology with graph theory (57M15) Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes (57-02)
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Cites Work
- ON A GENERALIZATION OF THE ALEXANDER POLYNOMIAL FOR LONG VIRTUAL KNOTS
- VIRTUAL CROSSING NUMBER AND THE ARROW POLYNOMIAL
- A polynomial invariant for knots via von Neumann algebras
- A new polynomial invariant of knots and links
- Connected Detachments of Graphs and Generalized Euler Trails
- THE TOPOLOGY OF SURFACES OF CONSTANT ENERGY IN INTEGRABLE HAMILTONIAN SYSTEMS, AND OBSTRUCTIONS TO INTEGRABILITY
- THE TOPOLOGY OF INTEGRAL SUBMANIFOLDS OF COMPLETELY INTEGRABLE HAMILTONIAN SYSTEMS
- Knots are Determined by Their Complements
- Skein quantization of Poisson algebras of loops on surfaces
- Braids, Links, and Mapping Class Groups. (AM-82)
- THE PLANARITY PROBLEM FOR SIGNED GAUSS WORDS
- Multimatroids I. Coverings by Independent Sets
- On the number of Euler trails in directed graphs
- MULTI-VARIABLE POLYNOMIAL INVARIANTS FOR VIRTUAL LINKS
- KAUFFMAN-LIKE POLYNOMIAL AND CURVES IN 2-SURFACES
- An Orientation-Sensitive Vassiliev Invariant for Virtual Knots
- Detecting Non-Triviality of Virtual Links
- ALEXANDER GROUPS AND VIRTUAL LINKS
- VASSILIEV KNOT INVARIANTS COMING FROM LIE ALGEBRAS AND 4-INVARIANTS
- ON HOMOLOGY OF VIRTUAL BRAIDS AND BURAU REPRESENTATION
- UNKNOTTING VIRTUAL KNOTS WITH GAUSS DIAGRAM FORBIDDEN MOVES
- INVARIANTS OF KNOT DIAGRAMS AND RELATIONS AMONG REIDEMEISTER MOVES
- ABSTRACT LINK DIAGRAMS AND VIRTUAL KNOTS
- VIRTUAL KNOT PRESENTATION OF RIBBON TORUS-KNOTS
- STABLE EQUIVALENCE OF KNOTS ON SURFACES AND VIRTUAL KNOT COBORDISMS
- DOES THE JONES POLYNOMIAL DETECT THE UNKNOT?
- PARITY AND EXOTIC COMBINATORIAL FORMULAE FOR FINITE-TYPE INVARIANTS OF VIRTUAL KNOTS
- Khovanov homology of graph-links
- LONG VIRTUAL KNOTS AND THEIR INVARIANTS
- CATEGORIFICATIONS OF THE COLORED JONES POLYNOMIAL
- The virtual and universal braids
- A conjecture on Khovanov's invariants
- A self-linking invariant of virtual knots
- Virtual braids
- Khovanov homology, its definitions and ramifications
- VASSILIEV INVARIANTS FOR VIRTUAL LINKS, CURVES ON SURFACES AND THE JONES–KAUFFMAN POLYNOMIAL
- New points of view in knot theory
- A Matrix Knot Invariant
- THE PLANARITY PROBLEM II
- Parity in knot theory
- Topology of words
- Parity, free knots, groups, and invariants of finite type
- A proof of Vassiliev's conjecture on the planarity of singular links
- Torsion of Khovanov homology
- Khovanov homology for virtual knots with arbitrary coefficients
- Matrix factorizations and link homology
- Link homology and Frobenius extensions
- VIRTUAL BRAIDS AND THE L-MOVE
- Link manifolds and periodicity
- A BRACKET POLYNOMIAL FOR GRAPHS, I
- Braid groups are linear
- Algorithmic topology and classification of 3-manifolds
- Braid groups are linear
- On lacets and their manifolds
- Bifurcations, atoms and knots
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- On long virtual knots
- An invariant of links in a thickened torus
- Algebraic structures on modules of diagrams
- Homotopy invariants of Gauss words
- Khovanov homology and the slice genus
- Free knots and groups
- Khovanov homology is an unknot-detector
- The classification of alternating links
- On the Jones polynomials of checkerboard colorable virtual links
- A functor-valued invariant of tangles
- Virtual knots and infinite-dimensional Lie algebras
- On minimal virtual link diagrams
- Theorie der Normalflächen. Ein Isotopiekriterium für den Kreisknoten
- Chords in a circle and linear algebra over GF(2)
- Invariants of virtual links
- Unoriented topological quantum field theory and link homology
- Curves on surfaces virtual knots, and the Jones-Kaufmann polynomial
- Finite-type invariants of virtual links and the Jones-Kauffman polynomial
- Some differentials on Khovanov-Rozansky homology
- Topological invariants of Liouville integrable Hamiltonian systems
- Matrix factorizations and link homology. II.
- On knot Floer width and Turaev genus
- Twisted link theory
- Additional gradings in the Khovanov complex for thickened surfaces
- Detecting the orientation of string links by finite type invariants
- The Khovanov complex and minimal knot diagrams
- Fixing the functoriality of Khovanov homology
- The Gauss code problem off the plane
- Invariant functions on Lie groups and Hamiltonian flows of surface group representations
- A spanning tree expansion of the Jones polynomial
- State models and the Jones polynomial
- Jones polynomials and classical conjectures in knot theory
- Hecke algebra representations of braid groups and link polynomials
- On the Kauffman polynomial of an adequate link
- Unimodularity and circle graphs
- A simple proof of the Murasugi and Kauffman theorems on alternating links
- Cycle decomposition by disjoint transpositions
- Principally unimodular skew-symmetric matrices
- Shortening curves on surfaces
- Circle graph obstructions
- The Conway polynomial in \(R^ 3\) and in thickened surfaces: A new determinant formulation
- What is a virtual link?
- On filamentations and virtual knots
- A few weight systems arising from intersection graphs
- Finite-type invariants of classical and virtual knots
- The bracket semigroup of knots
- On Khovanov's categorification of the Jones polynomial
- On invariants of virtual links
- Embeddings of 4-valent framed graphs into 2-surfaces
- A relation of Kauffman's \(f\)-polynomials of virtual links
- Categorification of the Kauffman bracket skein module of \(I\)-bundles over surfaces
- An invariant of link cobordisms from Khovanov homology
- Virtual strings.
- On the Vassiliev knot invariants
- Virtual knot theory
- Über Zopfgruppen und gleichsinnig verdrillte Verkettungen
- A virtualized skein relation for Jones polynomials
- The canonical genus of a classical and virtual knot
- Infinite families of links with trivial Jones polynomial
- Holomorphic disks and knot invariants
- On the Melvin-Morton-Rozansky conjecture
- Odd Khovanov homology
- A categorification of the Jones polynomial
- Binary nullity, Euler circuits and interlace polynomials
- Odd Khovanov homology is mutation invariant
- Atoms and minimal diagrams of virtual links
- Mutant knots and intersection graphs
- Braid presentation of virtual knots and welded knots
- Sur les difféomorphismes de la sphère de dimension trois \(\Gamma_ 4 = 0\)
- Minimal surface representations of virtual knots and links
- A BRACKET POLYNOMIAL FOR GRAPHS, III: VERTEX WEIGHTS
- Combinatorics and knot theory
- On Two Categorifications of the Arrow Polynomial for Virtual Knots
- AN EQUIVALENCE BETWEEN THE SET OF GRAPH-KNOTS AND THE SET OF HOMOTOPY CLASSES OF LOOPED GRAPHS
- Knot Theory
- Closed Curves That Never Extend to Proper Maps of Disks
- VIRTUAL KNOT DIAGRAMS AND THE WITTEN–RESHETIKHIN–TURAEV INVARIANT
- Virtual biquandles
- Flat hierarchy
- Virtual knot theory–-unsolved problems
- ALEXANDER GROUPS OF LONG VIRTUAL KNOTS
- ON VIRTUAL CROSSING NUMBER ESTIMATES FOR VIRTUAL LINKS
- INTRODUCTION TO GRAPH-LINK THEORY
- MAGNETIC GRAPHS AND AN INVARIANT FOR VIRTUAL LINKS
- Knots and words
- KHOVANOV HOMOLOGY FOR VIRTUAL KNOTS WITH ARBITRARY COEFFICIENTS
- The symplectic topology of completely integrable Hamiltonian systems
- THE VIRTUAL MAGNETIC KAUFFMAN BRACKET SKEIN MODULE AND SKEIN RELATIONS FOR THE f-POLYNOMIAL
- FREE KNOTS AND GROUPS
- AN ORIENTED MODEL FOR KHOVANOV HOMOLOGY
- A BRACKET POLYNOMIAL FOR GRAPHS, II: LINKS, EULER CIRCUITS AND MARKED GRAPHS
- A SPANNING TREE MODEL FOR KHOVANOV HOMOLOGY
- A MULTI-VARIABLE POLYNOMIAL INVARIANT FOR VIRTUAL KNOTS AND LINKS
- COBORDISMS OF WORDS
- Spanning trees and Khovanov homology
- On polynomial invariants of virtual links
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