Knot polynomials and Vassiliev's invariants
From MaRDI portal
Publication:2366468
DOI10.1007/BF01231287zbMath0812.57011OpenAlexW2082612727MaRDI QIDQ2366468
Publication date: 29 June 1993
Published in: Inventiones Mathematicae (Search for Journal in Brave)
Full work available at URL: https://eudml.org/doc/144077
Vassiliev invariantsJones' polynomialknot polynomialsspace of smooth maps from the circle to the 3-sphere
Spaces of embeddings and immersions (58D10) Embeddings in differential topology (57R40) Singularities of differentiable mappings in differential topology (57R45) Spectral sequences in algebraic topology (55T99)
Related Items
Improved bounds for colouring circle graphs ⋮ Kontsevich’s integral for the Kauffman polynomial ⋮ COEFFICIENTS OF HOMFLY POLYNOMIAL AND KAUFFMAN POLYNOMIAL ARE NOT FINITE TYPE INVARIANTS ⋮ Homflypt skein theory, string topology and 2-categories ⋮ THE CASSON–WALKER–LESCOP INVARIANT AND LINK INVARIANTS ⋮ Quantum enveloping superalgebras and link invariants ⋮ POLYAK TYPE EQUATIONS FOR VIRTUAL ARROW DIAGRAM INVARIANTS IN THE ANNULUS ⋮ Goussarov–Polyak–Viro conjecture for degree three case ⋮ ON A POINCARÉ POLYNOMIAL FROM KHOVANOV HOMOLOGY AND VASSILIEV INVARIANTS ⋮ Singquandle shadows and singular knot invariants ⋮ On the Jones polynomial modulo primes ⋮ Algebra, topology and the discoveries of Vaughan Jones ⋮ Combinatorial knot theory and the Jones polynomial ⋮ Delta Moves and Arrow Polynomials of Virtual Knots ⋮ The Jones polynomial, Knots, diagrams, and categories ⋮ Geodesic graphs for a homotopy class of virtual knots ⋮ On the skein theory of dichromatic links and invariants of finite type ⋮ Tackling tangledness of cosmic strings by knot polynomial topological invariants ⋮ Gauss diagram formulae for Vassiliev invariants from Kauffman polynomial ⋮ Lie algebra and Dynkin index ⋮ The coefficients of the Jones polynomial ⋮ Crossing change on Khovanov homology and a categorified Vassiliev skein relation ⋮ RIBBON-MOVES OF 2-LINKS PRESERVE THE μ-INVARIANT OF 2-LINKS ⋮ ON VASSILIEV INVARIANTS OF ORDER TWO FOR STRING LINKS ⋮ A POLYNOMIAL INVARIANT FOR LINKS IN LENS SPACES ⋮ Parity, free knots, groups, and invariants of finite type ⋮ Unnamed Item ⋮ Generating sets of Reidemeister moves of oriented singular links and quandles ⋮ C2, C3AND C4-MOVES AND THE COEFFICIENT OF THE CONWAY POLYNOMIAL FOR KNOTS ⋮ LENS KNOTS, PERIODIC LINKS AND VASSILIEV INVARIANTS ⋮ Local moves and restrictions on the Jones polynomial ⋮ TWIST MOVES AND VASSILIEV INVARIANTS ⋮ ON THE VASSILIEV INVARIANT OF TYPE 3 OF 2-BRIDGE KNOTS ⋮ Cn-MOVES, BRAID COMMUTATORS AND VASSILIEV KNOT INVARIANTS ⋮ The embedding space of hexagonal knots ⋮ VASSILIEV INVARIANTS FOR VIRTUAL LINKS, CURVES ON SURFACES AND THE JONES–KAUFFMAN POLYNOMIAL ⋮ Vassiliev invariants and the Poincaré conjecture ⋮ The universal finite-type invariant for braids, with integer coefficients ⋮ New points of view in knot theory ⋮ Topological invariants for superconducting cosmic strings ⋮ From chord parity to chord index ⋮ Tree invariants and Milnor linking numbers with indeterminacy ⋮ On the First Two Vassiliev Invariants ⋮ Knotting probability of equilateral hexagons ⋮ Any nontrivial knot projection with no triple chords has a monogon or a bigon ⋮ Unnamed Item ⋮ Intersection of two spheres in the metric space of knots by Cn-moves ⋮ Polynomial invariants of singular knots and links ⋮ Application of braiding sequences III: Concordance of positive knots ⋮ Cn-moves and the difference of Jones polynomials for links ⋮ THE MODULE OF TWO-CHORD DIAGRAMS FOR ORIENTED KNOTS OF ZERO WINDING NUMBER IN THE SOLID TORUS ⋮ \(C _{k}\)-moves on spatial theta-curves and Vassiliev invariants ⋮ Analysis of trapped entanglements in polymer networks. ⋮ Vassiliev knot invariants derived from cable \(\Gamma \)-polynomials ⋮ On Vassiliev knot invariants induced from finite type 3-manifold invariants ⋮ Finite-type invariants for graphs and graph reconstructions ⋮ Finite-type 1-cocycles of knots given by Polyak–Viro Formulas ⋮ KNOTS WITH GIVEN FINITE TYPE INVARIANTS AND Ck-DISTANCES ⋮ On universal Vassiliev invariants ⋮ Kontsevich's integral for the Homfly polynomial and relations between values of multiple zeta functions ⋮ Representation of the category of tangles by Kontsevich's iterated integral ⋮ The coloured Jones function ⋮ Knot Theory ⋮ ON THE Cn-DISTANCE AND VASSILIEV INVARIANTS ⋮ Vassiliev invariants for links from Chern-Simons perturbation theory ⋮ Higher order terms in the Melvin-Morton expansion of the colored Jones polynomial ⋮ Universal weight systems and the Melvin-Morton expansion of the colored Jones knot invariant ⋮ Involutory biquandles and singular knots and links ⋮ Computing Vassiliev's invariants ⋮ Elliptic KZ system, braid group of the torus and Vassiliev invariants ⋮ Yang–Baxter deformations and rack cohomology ⋮ On the quotients of cubic Hecke algebras ⋮ Bottom tangles and universal invariants ⋮ Models of random knots ⋮ A Kontsevich integral of order 1 ⋮ Parallel version of the universal Vassiliev-Kontsevich invariant ⋮ Pseudo diagrams of knots, links and spatial graphs ⋮ On the combinatorial structure of primitive Vassiliev invariants. II ⋮ Graph invariants of Vassiliev type and application to 4D quantum gravity ⋮ Galois relations on knot invariants ⋮ Off-shell color-kinematics duality for Chern-Simons ⋮ Finite type invariants of order 3 for a spatial handcuff graph ⋮ A finite type invariant of order at most 4 for genus 2 handlebody-knots is a constant map ⋮ An intrinsic approach to invariants of framed links in 3-manifolds ⋮ Differential operators and the wheels power series ⋮ WEIGHT SYSTEMS FOR MILNOR INVARIANTS ⋮ SIMILARITY INDICES OF AMPHICHEIRAL KNOTS AND TANGLES ⋮ A Cn-MOVE FOR A KNOT AND THE COEFFICIENTS OF THE CONWAY POLYNOMIAL ⋮ Application of Braiding Sequences. II. Polynomial Invariants of Positive Knots ⋮ Knots of genus one or on the number of alternating knots of given genus ⋮ A few weight systems arising from intersection graphs ⋮ Chord diagram invariants of tangles and graphs ⋮ INVARIANTS OF LINKS IN 3-MANIFOLDS AND SPLITTING PROBLEM OF TEXTILE STRUCTURES ⋮ Claspers and finite type invariants of links ⋮ Diagram invariants of knots and the Kontsevich integral ⋮ Finite type invariants for knotoids ⋮ Twisting of two strings and Vassiliev invariants ⋮ Bracket models for weight systems and the universal Vassiliev invariants ⋮ The first fundamental theorem of invariant theory for the orthosymplectic supergroup ⋮ Kauffman bracket of plane curves ⋮ Integration of singular braid invariants and graph cohomology ⋮ Algebraic structures on modules of diagrams ⋮ Topological insights from the Chinese Rings ⋮ On the calculation of the Kauffman bracket polynomial ⋮ Vassiliev invariants of type two for a link ⋮ Realization of Vassiliev invariants by unknotting number one knots ⋮ An introduction to the Abelian Reidemeister torsion of three-dimensional manifolds ⋮ Delta move and polynomial invariants of links ⋮ New perspectives on self-linking ⋮ Finite-type invariants for curves on surfaces ⋮ Vassiliev invariants of type one for links in the solid torus ⋮ \(C_n\)-moves and \(V_n\)-equivalence for links ⋮ \(SC_n\)-moves and the \((n+1)\)-st coefficients of the Conway polynomials of links ⋮ FINITE TYPE INVARIANTS OF LINKS WITH A FIXED LINKING MATRIX ⋮ A CHARACTERIZATION OF KNOTS IN A SPATIAL GRAPH II ⋮ Topologies on sets of polynomial knots and the homotopy types of the respective spaces ⋮ APPLICATION OF BRAIDING SEQUENCES, I: ON THE CHARACTERIZATION OF VASSILIEV AND POLYNOMIAL LINK INVARIANTS ⋮ Vassiliev Invariants and Similarity of Knots ⋮ A cobordism realizing crossing change on \(\mathfrak{sl}_2\) tangle homology and a categorified Vassiliev skein relation ⋮ A geometric characterization of Vassiliev invariants ⋮ The Jones polynomial of ribbon links ⋮ A two-variable series for knot complements ⋮ Singular link Floer homology ⋮ On the origin and development of subfactors and quantum topology ⋮ INTERSECTION GRAPHS FOR STRING LINKS ⋮ THE Ck-GORDIAN COMPLEX OF KNOTS ⋮ KNOTS WITH GIVEN FINITE TYPE INVARIANTS AND CONWAY POLYNOMIAL ⋮ RECOGNIZING TEXTILE STRUCTURES BY FINITE TYPE KNOT INVARIANTS ⋮ Skein quantization and lattice gauge field theory ⋮ Some remarks on the chord index ⋮ The Unknotting Problem ⋮ Numerical knot invariants of finite type from Chern-Simons perturbation theory ⋮ ON NORMALIZATIONS OF A REGULAR ISOTOPY INVARIANT FOR SPATIAL GRAPHS ⋮ A LOWER BOUND FOR THE NUMBER OF FORBIDDEN MOVES TO UNKNOT A LONG VIRTUAL KNOT ⋮ A two dimensional lattice of knots by C2m-moves ⋮ On finite type 3-manifold invariants. II ⋮ On derivatives of link polynomials ⋮ SIMPLIFIED NUMERICAL FORM OF UNIVERSAL FINITE TYPE INVARIANT OF GAUSS WORDS ⋮ Book Review: Introduction to Vassiliev knot invariants ⋮ VASSILIEV INVARIANTS AND SIMILARITY INDICES OF KNOTS, LINKS AND TANGLES ⋮ Combinatorial expression for universal Vassiliev link invariant ⋮ On a Hopf algebra in graph theory ⋮ An expansion of the Jones representation of genus \(2\) and the Torelli group ⋮ Computer evaluation of Kauffman polynomials by using Gauss codes, with a skein-template algorithm ⋮ Wheels, wheeling, and the Kontsevich integral of the unknot ⋮ THE JACOBI DIAGRAM FOR A Cn-MOVE AND THE HOMFLY POLYNOMIAL ⋮ q-DEFORMED SPIN NETWORKS, KNOT POLYNOMIALS AND ANYONIC TOPOLOGICAL QUANTUM COMPUTATION ⋮ Vassiliev invariants and knot polynomials ⋮ Two filtrations of ribbon 2-knots ⋮ On 1-handle surgery and finite type invariants of surface knots
Cites Work
- On knot invariants related to some statistical mechanical models
- Hecke algebra representations of braid groups and link polynomials
- Finite-type invariants of knots, links, and graphs
- A polynomial invariant for knots via von Neumann algebras
- A new polynomial invariant of knots and links
- Jones' Braid-Plat Formula and a New Surgery Triple
- New points of view in knot theory
- An Invariant of Regular Isotopy
- An invariant of spatial graphs
This page was built for publication: Knot polynomials and Vassiliev's invariants