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 2022-06-01 to 2026-06-01.)

Article	Citations
Vertex distortion detects the unknot	7
Connected sum and crossing numbers of flat virtual knots	7
Linking in tree-manifolds	5
Twisted Alexander invariants for the braid group associated with the Tong–Yang–Ma representation	5
The non-orientable 4-genus of 11 crossing non-alternating knots	5
Self-dual maps III: Projective links	4
A polynomial invariant of virtual links using Jager formula	4
New superbridge index calculations from non-minimal realizations	4
On the complexity of meander-like diagrams of knots	4
A note on the involutive invariants of certain pretzel knots	4
Knot types of two-strand-twisted torus knots	3
Multivariate Alexander quandles, IV. The medial quandle of a link	3
Conversion to almost classical virtual links and pseudo Goeritz matrices	3
On annulus presentations, dualizable patterns and RGB-diagrams	3
A spectrum connecting the bridge index and the braid index	3
Limits of the Tristram–Levine signature function	3
Conjugation in Sn	3
A combinatorial description of the LOSS Legendrian knot invariant	3
A multivariable polynomial invariant of virtual knots	3
Heegaard presentations and Milnor pairings of some knots	3
Invariants of flat connections on 4-manifolds from Hopf group-algebras	3
Embedding tangles in links and Gaussian integers	3
Signature and crossing number of links	3
Quandle action quivers	3
The F-polynomial invariant for knotoids	3

Memories of Vaughan Jones	2
Regular isotopy classes of link diagrams from Thompson’s groups	2
On the Upsilon invariant in grid homology	2
Quantum invariants of links and 3-manifolds with boundary defined via virtual links	2
One conjecture on cut points of virtual links and the arrow polynomial of twisted links	2
Knots with properties of a trefoil knot concerning unknotting operations	2
Gauss diagram formulae for Vassiliev invariants from Kauffman polynomial	2
Matrix representation for some generalized braid-like groups	2
Intersecting subgroups and symmetric commutator subgroups in virtual link groups	2
Algebra, topology and the discoveries of Vaughan Jones	2
Classifying links and spatial graphs with finite N -quandles	2
Pentagon equations, Delaunay triangulations and pure braid group invariant	2
Extremal Khovanov homology and the girth of a knot	2
Kirby–Thompson invariants of distant sums of standard surfaces	2
Remembering Vaughan Jones	2
A groupoid rack and spatial surfaces	2
The Rohlin invariant and ℤ/2-valued invariants of homology spheres	2
On some new oriented Singquandles and their shadows	2
An ????????2 action on link homology of T(2,k) torus links	2
A polynomial invariant of Kauffman type for knotoids	2
Decomposability of minimal defect branched coverings over the projective plane	2
Preface for Special Issue for Vaughan Jones	2
Generalization of arc shift for twisted knots	2
A new invariant of planar knotoids and finite-type invariants	2
On the geometry and bounded cohomology of racks and quandles	2
Group-valued invariant of knots in the full torus	2
Some experimental results on knots and links constructed from elements of Thompson’s group F à la Jones	2
Thistlethwaite theorems for knotoids and linkoids	2
A visit in Valparaíso	2
A note on Murasugi sum of trivially extendable relative trisections	2
Invariants of spatial graphs coming from maximal trees	2
Tri-plane diagrams for simple surfaces in S4	1
Cyclic sets from ribbon string links	1
Families of curly knots	1
Invariants of annular links, cobordisms and transverse links from combinatorial link Floer complex	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
Linking number for graph-links and some classification of graph-links	1
Carric mat and the further research on bipartite knots	1
Octahedral developing of knot complement II: Ptolemy coordinates and applications	1
On characterization of a multivariable polynomial invariant of twisted links	1
Relationship of the Hennings and Witten–Reshetikhan–Turaev invariants for higher rank quantum groups	1
Regular projections of the link L6n1	1
Jones rational coincidences	1
Author index Volume 32	1
A Seifert algorithm for integral homology spheres	1
On pretzel links which are concordant to the trivial link	1
On homogeneous quasipositive links	1
Simple braids tend toward positive entropy	1
From integrals to combinatorial formulas of finite type invariants — A case study	1

The special shadow-complexity of #k(S1 × S3)	1
An improvement of the lower bound for the minimum number of link colorings by quandles	1
Bi-Legendrian rack colorings of Legendrian knots	1
An invariant of free knots valued in non-abelian groups	1
A construction of multiple group racks	1
Link-homotopy classes of 4-component links, claspers and the Habegger–Lin algorithm	1
Left orderability for surgeries on the [1,1,2,2,2j] two-bridge knots	1
Reducible surgery in lens spaces and seiferters	1
Symmetry groups of hyperbolic links and their complements	1
Multivariate Alexander quandles, V. Constructing the medial quandle of a link	1
An algorithm to calculate generalized Seifert matrices	1
A universal algebraic approach to rack coverings	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
Computations of HOMFLY homology	1
Characterizing slopes for torus knots, II	1
Embedding Alexander quandles into groups	1
Multi-virtual knot theory	1
Computational complexity of graded knot invariant	1
Fibered 3-manifolds with unique incompressible surfaces	1
On the swap move of letters in words and the forbidden moves in virtual diagrams	1
In memory of Vaughan Jones	1
Two-bridge links and stable maps into the plane	1
Origins of the Temperley–Lieb algebra: Early history	1
Congruence subgroups of the virtual braid group	1
Alexander and Markov theorems for generalized knots, II generalized braids	1
Memories of Vaughan from his student days and after	1
The intersection polynomials of a virtual knot IV: Crossing change and supporting genus	1
Trisection embeddings of non-orientable 4-manifolds	1
Colorings of symmetric unions and partial knots	1
Positive braids minimize ascending number	1
KBSM for the family of small Seifert fibered 3-manifolds with multiplicity two exceptional fibers	1
Some generalizations of Satoh’s Tube map	1
Some polynomial invariants of virtual doodles	1
The one-row-colored ????????3 Jones polynomials for pretzel links	1
Erratum: Milnor’s triple linking number and Gauss diagram formulas of 3-bouquet graphs	1
Khovanov–Lipshitz–Sarkar homotopy type for links in thickened surfaces	1
Generalized knots–quivers correspondence	1
Periods of continued fractions and volumes of modular knots complements	1
A class of index polynomial invariants for virtual knots using flat virtual knots invariants	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
Shade quandle presentations for oriented links	1
Dynamics of quandle orders	1
Trisections induced by the Gluck surgery along certain spun knots	1
Region colorings of surfaces in 4-space	1
Orbits by the up–down action of braid diagrams	1
Richard A. Litherland: A brief biography	1
A Torres-type formula for the Alexander polynomial of spatial graphs	1
Personal recollection of Vaughan F. R. Jones (1952–2020)	1
Garside groups and geometry: Some thoughts for Patrick Dehornoy	1
Integer inequalities between knot invariants, skein tree depth and delta-crossing numbers	1
On the braid index of a two-bridge knot	1
B-type Catalan states of lattice crossing	1
The H(n)-move is an unknotting operation for virtual and welded links	1
A combinatorial proof of invariance of double-point enhanced grid homology	1