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 2022-05-01 to 2026-05-01.)

Article	Citations
New superbridge index calculations from non-minimal realizations	7
Vertex distortion detects the unknot	7
Connected sum and crossing numbers of flat virtual knots	5
Conjugation in S _n	4
The non-orientable 4-genus of 11 crossing non-alternating knots	4
Self-dual maps III: Projective links	4
A note on the involutive invariants of certain pretzel knots	4
Linking in tree-manifolds	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
Limits of the Tristram–Levine signature function	3
Embedding tangles in links and Gaussian integers	3
A spectrum connecting the bridge index and the braid index	3
Quandle action quivers	3
A combinatorial description of the LOSS Legendrian knot invariant	3
Invariants of flat connections on 4-manifolds from Hopf group-algebras	3
Multivariate Alexander quandles, IV. The medial quandle of a link	3
A multivariable polynomial invariant of virtual knots	3
On annulus presentations, dualizable patterns and RGB-diagrams	3
A polynomial invariant of virtual links using Jager formula	3
Signature and crossing number of links	3
Conversion to almost classical virtual links and pseudo Goeritz matrices	3
Heegaard presentations and Milnor pairings of some knots	3
Classifying links and spatial graphs with finite N -quandles	2
Decomposability of minimal defect branched coverings over the projective plane	2

Extremal Khovanov homology and the girth of a knot	2
A groupoid rack and spatial surfaces	2
Kirby–Thompson invariants of distant sums of standard surfaces	2
Remembering Vaughan Jones	2
A note on Murasugi sum of trivially extendable relative trisections	2
Thistlethwaite theorems for knotoids and linkoids	2
On some new oriented Singquandles and their shadows	2
Invariants of spatial graphs coming from maximal trees	2
Algebra, topology and the discoveries of Vaughan Jones	2
Trisection embeddings of non-orientable 4-manifolds	2
Preface for Special Issue for Vaughan Jones	2
Pentagon equations, Delaunay triangulations and pure braid group invariant	2
Generalization of arc shift for twisted knots	2
Intersecting subgroups and symmetric commutator subgroups in virtual link groups	2
A new invariant of planar knotoids and finite-type invariants	2
Group-valued invariant of knots in the full torus	2
On the geometry and bounded cohomology of racks and quandles	2
Matrix representation for some generalized braid-like groups	2
A visit in Valparaíso	2
An ????????2 action on link homology of T(2,k) torus links	2
Some experimental results on knots and links constructed from elements of Thompson’s group F à la Jones	2
Bi-Legendrian rack colorings of Legendrian knots	2
Quantum invariants of links and 3-manifolds with boundary defined via virtual links	2
Memories of Vaughan Jones	2
On the Upsilon invariant in grid homology	2
One conjecture on cut points of virtual links and the arrow polynomial of twisted links	2
Regular isotopy classes of link diagrams from Thompson’s groups	2
Knots with properties of a trefoil knot concerning unknotting operations	2
Gauss diagram formulae for Vassiliev invariants from Kauffman polynomial	2
The Rohlin invariant and ℤ/2-valued invariants of homology spheres	2
The F-polynomial invariant for knotoids	2
A polynomial invariant of Kauffman type for knotoids	2
Embedding tangles and the Kauffman bracket polynomials	2
Jones rational coincidences	1
Author index Volume 32	1
Some generalizations of Satoh’s Tube map	1
Two-bridge links and stable maps into the plane	1
Symmetry groups of hyperbolic links and their complements	1
Special Issue in Memory of Patrick Dehornoy	1
An algorithm to calculate generalized Seifert matrices	1
Cyclic sets from ribbon string links	1
Periods of continued fractions and volumes of modular knots complements	1
Origins of the Temperley–Lieb algebra: Early history	1
Invariants of annular links, cobordisms and transverse links from combinatorial link Floer complex	1
Region colorings of surfaces in 4-space	1
A Torres-type formula for the Alexander polynomial of spatial graphs	1
On homogeneous quasipositive links	1
A construction of multiple group racks	1
A combinatorial proof of invariance of double-point enhanced grid homology	1
A class of index polynomial invariants for virtual knots using flat virtual knots invariants	1

On characterization of a multivariable polynomial invariant of twisted links	1
Computational complexity of graded knot invariant	1
Carric mat and the further research on bipartite knots	1
The special shadow-complexity of #k(S1 × S3)	1
Colorings of symmetric unions and partial knots	1
Link-homotopy classes of 4-component links, claspers and the Habegger–Lin algorithm	1
Alexander and Markov theorems for generalized knots, II generalized braids	1
Linking number for graph-links and some classification of graph-links	1
Orbits by the up–down action of braid diagrams	1
On the swap move of letters in words and the forbidden moves in virtual diagrams	1
Counting the number of connected components of multi-curves through corresponding permutations	1
Simple braids tend toward positive entropy	1
The one-row-colored ????????3 Jones polynomials for pretzel links	1
Fibered 3-manifolds with unique incompressible surfaces	1
Tri-plane diagrams for simple surfaces in S4	1
Garside groups and geometry: Some thoughts for Patrick Dehornoy	1
Some polynomial invariants of virtual doodles	1
The intersection polynomials of a virtual knot IV: Crossing change and supporting genus	1
Multivariate Alexander quandles, V. Constructing the medial quandle of a link	1
Integer inequalities between knot invariants, skein tree depth and delta-crossing numbers	1
A note on Rivin’s interpretation of McShane’s identity as identities for closed geodesics with one self-intersection	1
Crossing numbers and rotation numbers of cycles in a plane immersed graph	1
The H(n)-move is an unknotting operation for virtual and welded links	1
In memory of Vaughan Jones	1
Computations of HOMFLY homology	1
Memories of Vaughan from his student days and after	1
B-type Catalan states of lattice crossing	1
Octahedral developing of knot complement II: Ptolemy coordinates and applications	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
Multi-virtual knot theory	1
Positive braids minimize ascending number	1
Trisections induced by the Gluck surgery along certain spun knots	1
Left orderability for surgeries on the [1,1,2,2,2j] two-bridge knots	1
On pretzel links which are concordant to the trivial link	1
Shade quandle presentations for oriented links	1
Families of curly knots	1
A universal algebraic approach to rack coverings	1
Representations of flat virtual braids which do not preserve the forbidden relations	1
Generalized knots–quivers correspondence	1
Khovanov–Lipshitz–Sarkar homotopy type for links in thickened surfaces	1
On the braid index of a two-bridge knot	1
Regular projections of the link L6n1	1
Characterizing slopes for torus knots, II	1
A Seifert algorithm for integral homology spheres	1
Erratum: Milnor’s triple linking number and Gauss diagram formulas of 3-bouquet graphs	1
Richard A. Litherland: A brief biography	1
KBSM for the family of small Seifert fibered 3-manifolds with multiplicity two exceptional fibers	1
From integrals to combinatorial formulas of finite type invariants — A case study	1
An improvement of the lower bound for the minimum number of link colorings by quandles	1
Classification of doubly periodic untwisted (p,q)-weaves by their crossing number and matrices	1
Dynamics of quandle orders	1
Reducible surgery in lens spaces and seiferters	1
An invariant of free knots valued in non-abelian groups	1
Embedding Alexander quandles into groups	1
Relationship of the Hennings and Witten–Reshetikhan–Turaev invariants for higher rank quantum groups	1
Congruence subgroups of the virtual braid group	1