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 2021-10-01 to 2025-10-01.)

Article	Citations
Vertex distortion detects the unknot	7
A Polynomial Invariant of Virtual Links Using Jager Formula	7
A note on the involutive invariants of certain pretzel knots	7
Linking in tree-manifolds	6
Virtual index cocycles and invariants of virtual links	5
The non-orientable 4-genus of 11 crossing non-alternating knots	5
New superbridge index calculations from non-minimal realizations	4
A spectrum connecting the bridge index and the braid index	4
Connected sum and crossing numbers of flat virtual knots	4
On the Complexity of Meander-like Diagrams of Knots	4
Twisted Alexander invariants for the braid group associated with the Tong–Yang–Ma representation	4
Embedding tangles in links and Gaussian integers	4
Self-dual maps III: Projective links	4
Multivariate Alexander quandles, IV. The medial quandle of a link	3
Conversion to almost classical virtual links and pseudo Goeritz matrices	3
A combinatorial description of the LOSS Legendrian knot invariant	3
A multivariable polynomial invariant of virtual knots	3
Limits of the Tristram–Levine signature function	3
On annulus presentations, dualizable patterns and RGB-diagrams	2
Matrix representation for some generalized braid-like groups	2
Forty years in mathematics: Personal perspective (Part I)	2
Decomposability of minimal defect branched coverings over the projective plane	2
A note on Murasugi sum of trivially extendable relative trisections	2
Remembering Vaughan Jones	2
Some experimental results on knots and links constructed from elements of Thompson’s group F à la Jones	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
The F-polynomial invariant for knotoids	2
Quandle action quivers	2
Invariants of spatial graphs coming from maximal trees	2
Regular isotopy classes of link diagrams from Thompson’s groups	2
Algebra, topology and the discoveries of Vaughan Jones	2
Pentagon equations, Delaunay triangulations and pure braid group invariant	2
On the geometry and bounded cohomology of racks and quandles	2
Embedding tangles and the Kauffman bracket polynomials	2
Intersecting subgroups and symmetric commutator subgroups in virtual link groups	2
Knots with properties of a trefoil knot concerning unknotting operations	2
A visit in Valparaíso	2
Heegaard presentations and Milnor pairings of some knots	2
Preface	2
A new invariant of planar knotoids and finite-type invariants	2
Classifying links and spatial graphs with finite N-quandles	2
Quantum invariants of links and 3-manifolds with boundary defined via virtual links	2
Generalization of arc shift for twisted knots	2
One conjecture on cut points of virtual links and the arrow polynomial of twisted links	2
A groupoid rack and spatial surfaces	2
A polynomial invariant of Kauffman type for knotoids	2
Integral geometric orbifolds	2
On some new oriented Singquandles and their shadows	2
Gauss diagram formulae for Vassiliev invariants from Kauffman polynomial	2
Cyclic sets from ribbon string links	1
Multi-virtual knot theory	1
In Memory of Vaughan Jones (Renzo L. Ricca)	1
Memories of Vaughan Jones	1
Special Issue in Memory of Patrick Dehornoy	1
A construction of multiple group racks	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
The H(n)-move is an unknotting operation for virtual and welded links	1
Left orderability for surgeries on the [1,1,2,2,2j] two-bridge knots	1
Bi-Legendrian rack colorings of Legendrian knots	1
The special shadow-complexity of #k(S1 × S3)	1
Garside groups and geometry: Some thoughts for Patrick Dehornoy	1
Relationship of the Hennings and Witten–Reshetikhan–Turaev invariants for higher rank quantum groups	1
Classification of doubly periodic untwisted (p,q)-weaves by their crossing number and matrices	1
On the braid index of a two-bridge knot	1
Embedding Alexander quandles into groups	1
Properties of minimal charts and their applications VIII: Charts of type (7)	1
Regular projections of the link L6n1	1
Carric mat and the further research on bipatite knots	1
A Seifert algorithm for integral homology spheres	1
On pretzel links which are concordant to the trivial link	1
Author index Volume 32	1
Fibered 3-manifolds with unique incompressible surfaces	1
A universal algebraic approach to rack coverings	1

Shade quandle presentations for oriented links	1
Periods of continued fractions and volumes of modular knots complements	1
On homogeneous quasipositive links	1
An algorithm to calculate generalized Seifert matrices	1
Preface for Special Issue for Vaughan Jones	1
Jones rational coincidences	1
Characterizing slopes for torus knots, II	1
Khovanov-Lipshitz-Sarkar Homotopy type for links in thickened surfaces and those in S³ with new modulis	1
Knot cobordism and Lee’s perturbation of Khovanov homology	1
Positive braids minimize ascending number	1
Multivariate Alexander quandles, V. Constructing the medial quandle of a link	1
Simple braids tend toward positive entropy	1
A Torres-type formula for the Alexander polynomial of spatial graphs	1
Representations of flat virtual braids which do not preserve the forbidden relations	1
A note on Rivin’s interpretation of McShane’s identity as identities for closed geodesics with one self-intersection	1
The one-row-colored ????????3 Jones polynomials for pretzel links	1
A class of index polynomial invariants for virtual knots using flat virtual knots invariants	1
Some generalizations of Satoh’s Tube map	1
Finite involutory quandles of two-bridge links with an axis	1
Computations of HOMFLY homology	1
Counting the number of connected components of multi-curves through corresponding permutations	1
Two-bridge links and stable maps into the plane	1
The intersection polynomials of a virtual knot IV: Crossing change and supporting genus	1
Reducible surgery in lens spaces and seiferters	1
Trisection embeddings of non-orientable 4-manifolds	1
On the swap move of letters in words and the forbidden moves in virtual diagrams	1
Orbits by the up–down action of braid diagrams	1
Tri-plane diagrams for simple surfaces in S4	1
Families of curly knots	1
Extremal Khovanov homology and the girth of a knot	1
A combinatorial proof of invariance of double-point enhanced grid homology	1
Invariants of annular links, cobordisms and transverse links from combinatorial link Floer complex	1
Coefficients of catalan states without nesting and maximal number of returns	1
Some polynomial invariants of virtual doodles	1
B-type Catalan states of lattice crossing	1
Erratum: Milnor’s triple linking number and Gauss diagram formulas of 3-bouquet graphs	1
Linking number for graph-links and some classification of graph-links	1
Octahedral developing of knot complement II: Ptolemy coordinates and applications	1
Symmetry groups of hyperbolic links and their complements	1
Signed heights of knotoids	1
Memories of Vaughan from his student days and after	1
The Jones polynomials of three-bridge knots via Chebyshev knots and billiard table diagrams	1
Generalized knots–quivers correspondence	1
An improvement of the lower bound for the minimum number of link colorings by quandles	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
Alexander and Markov theorems for generalized knots, II generalized braids	1