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 2021-08-01 to 2025-08-01.)

Article	Citations
The non-orientable 4-genus of 11 crossing non-alternating knots	7
A note on the involutive invariants of certain pretzel knots	7
A Polynomial Invariant of Virtual Links Using Jager Formula	7
Virtual index cocycles and invariants of virtual links	6
New superbridge index calculations from non-minimal realizations	5
Twisted Alexander invariants for the braid group associated with the Tong–Yang–Ma representation	5
A Spectrum Connecting the Bridge Index and the Braid Index	4
Limits of the Tristram–Levine signature function	4
Linking in tree-manifolds	4
Multivariate Alexander quandles, IV. The medial quandle of a link	4
Self-dual maps III: Projective links	4
Vertex distortion detects the unknot	4
A combinatorial description of the LOSS Legendrian knot invariant	4
Connected sum and crossing numbers of flat virtual knots	4
Gauss diagram formulae for Vassiliev invariants from Kauffman polynomial	3
Embedding tangles in links and Gaussian integers	3
A visit in Valparaíso	3
The F-polynomial invariant for knotoids	3
Conversion to almost classical virtual links and pseudo Goeritz matrices	3
Local-moves on knots and products of knots II	2
Regular isotopy classes of link diagrams from Thompson’s groups	2
Extremal Khovanov homology and the girth of a knot	2
Pentagon equations, Delaunay triangulations and pure braid group invariant	2
One conjecture on cut points of virtual links and the arrow polynomial of twisted links	2
Algebra, topology and the discoveries of Vaughan Jones	2

A note on Murasugi sum of trivially extendable relative trisections	2
Group-valued invariant of knots in the full torus	2
The Rohlin invariant and ℤ/2-valued invariants of homology spheres	2
On linear resolvability of universal quantum dimensions	2
Heegaard presentations and Milnor pairings of some knots	2
A diagrammatic presentation and its characterization of non-split compact surfaces in the 3-sphere	2
Bi-Legendrian rack colorings of Legendrian knots	2
Preface	2
Knots with properties of a trefoil knot concerning unknotting operations	2
Remembering Vaughan Jones	2
A new invariant of planar knotoids and finite-type invariants	2
Forty years in mathematics: Personal perspective (Part I)	2
On some new oriented Singquandles and their shadows	2
Integral geometric orbifolds	2
Quandle action quivers	2
Embedding tangles and the Kauffman bracket polynomials	2
Quantum invariants of links and 3-manifolds with boundary defined via virtual links	2
Preface for Special Issue for Vaughan Jones	2
Generalization of arc shift for twisted knots	2
A groupoid rack and spatial surfaces	2
Intersecting subgroups and symmetric commutator subgroups in virtual link groups	2
Invariants of spatial graphs coming from maximal trees	2
On the geometry and bounded cohomology of racks and quandles	2
A multivariable polynomial invariant of virtual knots	2
On annulus presentations, dualizable patterns and RGB-diagrams	2
A polynomial invariant of Kauffman type for knotoids	2
Characterizing slopes for torus knots, II	1
In Memory of Vaughan Jones (Renzo L. Ricca)	1
Some polynomial invariants of virtual doodles	1
B-type Catalan states of lattice crossing	1
Knot cobordism and Lee’s perturbation of Khovanov homology	1
An algorithm to calculate generalized Seifert matrices	1
A note on Rivin’s interpretation of McShane’s identity as identities for closed geodesics with one self-intersection	1
Counting the number of connected components of multi-curves through corresponding permutations	1
The one-row-colored ????????3 Jones polynomials for pretzel links	1
A Torres-type formula for the Alexander polynomial of spatial graphs	1
Linking number for graph-links and some classification of graph-links	1
On hyperelliptic Euclidean 3-manifolds	1
Families of curly knots	1
Reducible surgery in lens spaces and seiferters	1
Author index Volume 32	1
On the braid index of a two-bridge knot	1
Regular projections of the link L6n1	1
Alexander and Markov theorems for generalized knots, II generalized braids	1
On homogeneous quasipositive links	1
Octahedral developing of knot complement II: Ptolemy coordinates and applications	1
Lefschetz open book decompositions of 4-manifolds	1
Generalized knots–quivers correspondence	1
Personal recollection of Vaughan F. R. Jones (1952–2020)	1
Multi-virtual knot theory	1

Signed heights of knotoids	1
The H(n)-move is an unknotting operation for virtual and welded links	1
An improvement of the lower bound for the minimum number of link colorings by quandles	1
Cyclic sets from ribbon string links	1
Relationship of the Hennings and Witten–Reshetikhan–Turaev invariants for higher rank quantum groups	1
Erratum: Milnor’s triple linking number and Gauss diagram formulas of 3-bouquet graphs	1
Properties of minimal charts and their applications VIII: Charts of type (7)	1
Periods of continued fractions and volumes of modular knots complements	1
Tri-plane diagrams for simple surfaces in S4	1
Connected sum of virtual knots and F-polynomials	1
Symmetry groups of hyperbolic links and their complements	1
A universal algebraic approach to rack coverings	1
Orbits by the up–down action of braid diagrams	1
Memories of Vaughan from his student days and after	1
On the swap move of letters in words and the forbidden moves in virtual diagrams	1
On pretzel links which are concordant to the trivial link	1
Shade quandle presentations for oriented links	1
Special Issue in Memory of Patrick Dehornoy	1
Crossing numbers and rotation numbers of cycles in a plane immersed graph	1
Jones rational coincidences	1
The photography method: Solving pentagon equation	1
The special shadow-complexity of #k(S1 × S3)	1
Simple braids tend toward positive entropy	1
Memories of Vaughan Jones	1
The intersection polynomials of a virtual knot IV: Crossing change and supporting genus	1
Invariants of annular links, cobordisms and transverse links from combinatorial link Floer complex	1
Left orderability for surgeries on the [1,1,2,2,2j] two-bridge knots	1
A class of index polynomial invariants for virtual knots using flat virtual knots invariants	1
Coefficients of catalan states without nesting and maximal number of returns	1
Classification of doubly periodic untwisted (p,q)-weaves by their crossing number and matrices	1
Some generalizations of Satoh’s Tube map	1
Fibered 3-manifolds with unique incompressible surfaces	1
Computations of HOMFLY homology	1
Representations of flat virtual braids which do not preserve the forbidden relations	1
Carric mat and the further research on bipatite knots	1
Multivariate Alexander quandles, V. Constructing the medial quandle of a link	1
The Jones polynomials of three-bridge knots via Chebyshev knots and billiard table diagrams	1
Garside groups and geometry: Some thoughts for Patrick Dehornoy	1
A Seifert algorithm for integral homology spheres	1
A combinatorial proof of invariance of double-point enhanced grid homology	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
Trisections induced by the Gluck surgery along certain spun knots	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
Biquandle brackets and knotoids	1
Two-bridge links and stable maps into the plane	1
On invariants of surfaces in the 3-sphere	1
Embedding Alexander quandles into groups	1
From integrals to combinatorial formulas of finite type invariants — A case study	1