OOIR: Observatory of International Research

Papers

(The TQCC of Journal of Knot Theory and Its Ramifications is 1. The table below lists those papers that are above that threshold based on CrossRef citation counts [max. 250 papers]. The publications cover those that have been published in the past four years, i.e., from 2021-07-01 to 2025-07-01.)

Article	Citations
Twisted Alexander invariants for the braid group associated with the Tong–Yang–Ma representation	7
A Polynomial Invariant of Virtual Links Using Jager Formula	7
A note on the involutive invariants of certain pretzel knots	7
Self-dual maps III: Projective links	6
Connected sum and crossing numbers of flat virtual knots	5
The non-orientable 4-genus of 11 crossing non-alternating knots	5
Linking in tree-manifolds	4
Virtual index cocycles and invariants of virtual links	4
Vertex distortion detects the unknot	4
A Spectrum Connecting the Bridge Index and the Braid Index	4
New superbridge index calculations from non-minimal realizations	4
Limits of the Tristram–Levine signature function	3
Integral geometric orbifolds	3
Embedding tangles in links and Gaussian integers	3
Multivariate Alexander quandles, IV. The medial quandle of a link	3
A combinatorial description of the LOSS Legendrian knot invariant	3
A visit in Valparaíso	3
Quantum invariants of links and 3-manifolds with boundary defined via virtual links	2
Regular isotopy classes of link diagrams from Thompson’s groups	2
Generalization of arc shift for twisted knots	2
A note on Murasugi sum of trivially extendable relative trisections	2
A groupoid rack and spatial surfaces	2
Invariants of spatial graphs coming from maximal trees	2
Forty years in mathematics: Personal perspective (Part I)	2
The F-polynomial invariant for knotoids	2

On linear resolvability of universal quantum dimensions	2
Heegaard presentations and Milnor pairings of some knots	2
On annulus presentations, dualizable patterns and RGB-diagrams	2
Embedding tangles and the Kauffman bracket polynomials	2
Pentagon equations, Delaunay triangulations and pure braid group invariant	2
Bi-Legendrian rack colorings of Legendrian knots	2
A new invariant of planar knotoids and finite-type invariants	2
A polynomial invariant of Kauffman type for knotoids	2
Quandle action quivers	2
Algebra, topology and the discoveries of Vaughan Jones	2
Preface	2
On some new oriented Singquandles and their shadows	2
Gauss diagram formulae for Vassiliev invariants from Kauffman polynomial	2
A multivariable polynomial invariant of virtual knots	2
A diagrammatic presentation and its characterization of non-split compact surfaces in the 3-sphere	2
Group-valued invariant of knots in the full torus	2
Preface for Special Issue for Vaughan Jones	2
Extremal Khovanov homology and the girth of a knot	2
Intersecting subgroups and symmetric commutator subgroups in virtual link groups	2
On the geometry and bounded cohomology of racks and quandles	2
One conjecture on cut points of virtual links and the arrow polynomial of twisted links	2
Remembering Vaughan Jones	2
Conversion to almost classical virtual links and pseudo Goeritz matrices	2
The Rohlin invariant and ℤ/2-valued invariants of homology spheres	2
Knots with properties of a trefoil knot concerning unknotting operations	2
Local-moves on knots and products of knots II	2
A Torres-type formula for the Alexander polynomial of spatial graphs	1
Connected sum of virtual knots and F-polynomials	1
Linking number for graph-links and some classification of graph-links	1
Properties of minimal charts and their applications VIII: Charts of type (7)	1
Alexander and Markov theorems for generalized knots, II generalized braids	1
Families of curly knots	1
Special Issue in Memory of Patrick Dehornoy	1
An algorithm to calculate generalized Seifert matrices	1
In Memory of Vaughan Jones (Renzo L. Ricca)	1
Simple braids tend toward positive entropy	1
Finite involutory quandles of two-bridge links with an axis	1
Link-homotopy classes of 4-component links, claspers and the Habegger–Lin algorithm	1
Memories of Vaughan from his student days and after	1
Regular projections of the link L6n1	1
Memories of Vaughan Jones	1
Biquandle brackets and knotoids	1
Characterizing slopes for torus knots, II	1
Crossing numbers and rotation numbers of cycles in a plane immersed graph	1
The special shadow-complexity of #k(S1 × S3)	1
A combinatorial proof of invariance of double-point enhanced grid homology	1
Multivariate Alexander quandles, V. Constructing the medial quandle of a link	1
On the swap move of letters in words and the forbidden moves in virtual diagrams	1
The H(n)-move is an unknotting operation for virtual and welded links	1
B-type Catalan states of lattice crossing	1

Generalized knots-quivers correspondence	1
Carric mat and the further research on bipatite knots	1
Counting the number of connected components of multi-curves through corresponding permutations	1
Tri-plane diagrams for simple surfaces in S4	1
Two-bridge links and stable maps into the plane	1
Multi-virtual knot theory	1
Symmetry groups of hyperbolic links and their complements	1
Fibered 3-manifolds with unique incompressible surfaces	1
Shade quandle presentations for oriented links	1
Representations of flat virtual braids which do not preserve the forbidden relations	1
Jones rational coincidences	1
Embedding Alexander quandles into groups	1
On homogeneous quasipositive links	1
Periods of continued fractions and volumes of modular knots complements	1
An improvement of the lower bound for the minimum number of link colorings by quandles	1
Orbits by the up–down action of braid diagrams	1
Personal recollection of Vaughan F. R. Jones (1952–2020)	1
Knot cobordism and Lee’s perturbation of Khovanov homology	1
The photography method: Solving pentagon equation	1
A class of index polynomial invariants for virtual knots using flat virtual knots invariants	1
Twisted cohomology pairings of knots II; to some Blanchfield pairings	1
A note on Rivin’s interpretation of McShane’s identity as identities for closed geodesics with one self-intersection	1
Author index Volume 32	1
Reducible surgery in lens spaces and seiferters	1
Garside groups and geometry: Some thoughts for Patrick Dehornoy	1
The one-row-colored ????????3 Jones polynomials for pretzel links	1
Octahedral developing of knot complement II: Ptolemy coordinates and applications	1
Invariants of annular links, cobordisms and transverse links from combinatorial link Floer complex	1
Some generalizations of Satoh’s Tube map	1
Relationship of the Hennings and Witten–Reshetikhan–Turaev invariants for higher rank quantum groups	1
A universal algebraic approach to rack coverings	1
Left orderability for surgeries on the [1,1,2,2,2j] two-bridge knots	1
The Jones polynomials of three-bridge knots via Chebyshev knots and billiard table diagrams	1
On pretzel links which are concordant to the trivial link	1
Signed heights of knotoids	1
Coefficients of catalan states without nesting and maximal number of returns	1
Torus knots and links in V1 that are invariant under the ℤm × ℤl-actions on V1 that form the quotient orbifold (A0,k)	1
On the braid index of a two-bridge knot	1
A complete list of minimal diagrams of an oriented alternating knot	1
On hyperelliptic Euclidean 3-manifolds	1
Trisections induced by the Gluck surgery along certain spun knots	1
Erratum: Milnor’s triple linking number and Gauss diagram formulas of 3-bouquet graphs	1
On invariants of surfaces in the 3-sphere	1
Classification of doubly periodic untwisted (p,q)-weaves by their crossing number and matrices	1
Lefschetz open book decompositions of 4-manifolds	1
Some polynomial invariants of virtual doodles	1
The intersection polynomials of a virtual knot IV: Crossing change and supporting genus	1
Cyclic sets from ribbon string links	1
A Seifert algorithm for integral homology spheres	1