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
Vertex distortion detects the unknot	7
New superbridge index calculations from non-minimal realizations	7
Connected sum and crossing numbers of flat virtual knots	5
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
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 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
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
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
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
A Torres-type formula for the Alexander polynomial of spatial graphs	1
Multi-virtual knot theory	1
A construction of multiple group racks	1
Left orderability for surgeries on the [1,1,2,2,2j] two-bridge knots	1
On characterization of a multivariable polynomial invariant of twisted links	1
Families of curly knots	1
A class of index polynomial invariants for virtual knots using flat virtual knots invariants	1
Representations of flat virtual braids which do not preserve the forbidden relations	1
Carric mat and the further research on bipartite knots	1
The special shadow-complexity of #k(S1 × S3)	1
Khovanov–Lipshitz–Sarkar homotopy type for links in thickened surfaces	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
Regular projections of the link L6n1	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
A Seifert algorithm for integral homology spheres	1

Simple braids tend toward positive entropy	1
Fibered 3-manifolds with unique incompressible surfaces	1
Richard A. Litherland: A brief biography	1
Garside groups and geometry: Some thoughts for Patrick Dehornoy	1
From integrals to combinatorial formulas of finite type invariants — A case study	1
Some polynomial invariants of virtual doodles	1
An improvement of the lower bound for the minimum number of link colorings by quandles	1
Multivariate Alexander quandles, V. Constructing the medial quandle of a link	1
An invariant of free knots valued in non-abelian groups	1
A note on Rivin’s interpretation of McShane’s identity as identities for closed geodesics with one self-intersection	1
Congruence subgroups of the virtual braid group	1
The H(n)-move is an unknotting operation for virtual and welded links	1
Some generalizations of Satoh’s Tube map	1
Symmetry groups of hyperbolic links and their complements	1
Computations of HOMFLY homology	1
Memories of Vaughan from his student days and after	1
An algorithm to calculate generalized Seifert matrices	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
Positive braids minimize ascending number	1
Trisections induced by the Gluck surgery along certain spun knots	1
Origins of the Temperley–Lieb algebra: Early history	1
On pretzel links which are concordant to the trivial link	1
Shade quandle presentations for oriented links	1
A universal algebraic approach to rack coverings	1
Region colorings of surfaces in 4-space	1
Generalized knots–quivers correspondence	1
On homogeneous quasipositive links	1
On the braid index of a two-bridge knot	1
A combinatorial proof of invariance of double-point enhanced grid homology	1
Characterizing slopes for torus knots, II	1
Computational complexity of graded knot invariant	1
Erratum: Milnor’s triple linking number and Gauss diagram formulas of 3-bouquet graphs	1
Colorings of symmetric unions and partial knots	1
KBSM for the family of small Seifert fibered 3-manifolds with multiplicity two exceptional fibers	1
Linking number for graph-links and some classification of graph-links	1
Classification of doubly periodic untwisted (p,q)-weaves by their crossing number and matrices	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
Dynamics of quandle orders	1
Reducible surgery in lens spaces and seiferters	1
Tri-plane diagrams for simple surfaces in S4	1
Embedding Alexander quandles into groups	1
Relationship of the Hennings and Witten–Reshetikhan–Turaev invariants for higher rank quantum groups	1
Jones rational coincidences	1
Author index Volume 32	1
The intersection polynomials of a virtual knot IV: Crossing change and supporting genus	1
Two-bridge links and stable maps into the plane	1
Special Issue in Memory of Patrick Dehornoy	1
Integer inequalities between knot invariants, skein tree depth and delta-crossing numbers	1
Cyclic sets from ribbon string links	1
Crossing numbers and rotation numbers of cycles in a plane immersed graph	1
Periods of continued fractions and volumes of modular knots complements	1
In memory of Vaughan Jones	1
Invariants of annular links, cobordisms and transverse links from combinatorial link Floer complex	1
B-type Catalan states of lattice crossing	1