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 2021-11-01 to 2025-11-01.)

Article	Citations
Vertex distortion detects the unknot	7
Self-dual maps III: Projective links	7
Connected sum and crossing numbers of flat virtual knots	5
Linking in tree-manifolds	5
A Polynomial Invariant of Virtual Links Using Jager Formula	4
Virtual index cocycles and invariants of virtual links	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
The non-orientable 4-genus of 11 crossing non-alternating knots	4
A note on the involutive invariants of certain pretzel knots	4
New superbridge index calculations from non-minimal realizations	4
A combinatorial description of the LOSS Legendrian knot invariant	3
Limits of the Tristram–Levine signature function	3
Multivariate Alexander quandles, IV. The medial quandle of a link	3
Embedding tangles in links and Gaussian integers	3
A spectrum connecting the bridge index and the braid index	3
Preface	2
Preface for Special Issue for Vaughan Jones	2
Extremal Khovanov homology and the girth of a knot	2
Classifying links and spatial graphs with finite N-quandles	2
A new invariant of planar knotoids and finite-type invariants	2
Forty years in mathematics: Personal perspective (Part I)	2
Intersecting subgroups and symmetric commutator subgroups in virtual link groups	2
On some new oriented Singquandles and their shadows	2
A multivariable polynomial invariant of virtual knots	2

On annulus presentations, dualizable patterns and RGB-diagrams	2
Conversion to almost classical virtual links and pseudo Goeritz matrices	2
Remembering Vaughan Jones	2
One conjecture on cut points of virtual links and the arrow polynomial of twisted links	2
Quantum invariants of links and 3-manifolds with boundary defined via virtual links	2
Pentagon equations, Delaunay triangulations and pure braid group invariant	2
Embedding tangles and the Kauffman bracket polynomials	2
A groupoid rack and spatial surfaces	2
Invariants of spatial graphs coming from maximal trees	2
Matrix representation for some generalized braid-like groups	2
Some experimental results on knots and links constructed from elements of Thompson’s group F à la Jones	2
Knots with properties of a trefoil knot concerning unknotting operations	2
The F-polynomial invariant for knotoids	2
On linear resolvability of universal quantum dimensions	2
Group-valued invariant of knots in the full torus	2
Algebra, topology and the discoveries of Vaughan Jones	2
Memories of Vaughan Jones	2
Bi-Legendrian rack colorings of Legendrian knots	2
Generalization of arc shift for twisted knots	2
A polynomial invariant of Kauffman type for knotoids	2
On the geometry and bounded cohomology of racks and quandles	2
A note on Murasugi sum of trivially extendable relative trisections	2
The Rohlin invariant and ℤ/2-valued invariants of homology spheres	2
A visit in Valparaíso	2
Heegaard presentations and Milnor pairings of some knots	2
Quandle action quivers	2
Gauss diagram formulae for Vassiliev invariants from Kauffman polynomial	2
Memories of Vaughan from his student days and after	1
Positive braids minimize ascending number	1
Khovanov–Lipshitz–Sarkar homotopy type for links in thickened surfaces	1
Trisection embeddings of non-orientable 4-manifolds	1
Tri-plane diagrams for simple surfaces in S4	1
Some polynomial invariants of virtual doodles	1
Jones rational coincidences	1
An algorithm to calculate generalized Seifert matrices	1
Invariants of annular links, cobordisms and transverse links from combinatorial link Floer complex	1
The Jones polynomials of three-bridge knots via Chebyshev knots and billiard table diagrams	1
Linking number for graph-links and some classification of graph-links	1
Periods of continued fractions and volumes of modular knots complements	1
On homogeneous quasipositive links	1
A class of index polynomial invariants for virtual knots using flat virtual knots invariants	1
The H(n)-move is an unknotting operation for virtual and welded links	1
Signed heights of knotoids	1
A universal algebraic approach to rack coverings	1
Trisections induced by the Gluck surgery along certain spun knots	1
Regular isotopy classes of link diagrams from Thompson’s groups	1
Origins of the Temperley-Lieb Algebra: Early History	1
Orbits by the up–down action of braid diagrams	1
Colorings of Symmetric Unions and Partial Knots	1
A Torres-type formula for the Alexander polynomial of spatial graphs	1

Garside groups and geometry: Some thoughts for Patrick Dehornoy	1
Representations of flat virtual braids which do not preserve the forbidden relations	1
Special Issue in Memory of Patrick Dehornoy	1
B-type Catalan states of lattice crossing	1
Families of curly knots	1
The special shadow-complexity of #k(S1 × S3)	1
Relationship of the Hennings and Witten–Reshetikhan–Turaev invariants for higher rank quantum groups	1
Characterizing slopes for torus knots, II	1
Some generalizations of Satoh’s Tube map	1
Counting the number of connected components of multi-curves through corresponding permutations	1
Erratum: Milnor’s triple linking number and Gauss diagram formulas of 3-bouquet graphs	1
In Memory of Vaughan Jones (Renzo L. Ricca)	1
Knot cobordism and Lee’s perturbation of Khovanov homology	1
A Seifert algorithm for integral homology spheres	1
Octahedral developing of knot complement II: Ptolemy coordinates and applications	1
Multivariate Alexander quandles, V. Constructing the medial quandle of a link	1
Shade quandle presentations for oriented links	1
Computations of HOMFLY homology	1
The intersection polynomials of a virtual knot IV: Crossing change and supporting genus	1
Fibered 3-manifolds with unique incompressible surfaces	1
On the braid index of a two-bridge knot	1
On pretzel links which are concordant to the trivial link	1
On the swap move of letters in words and the forbidden moves in virtual diagrams	1
Simple braids tend toward positive entropy	1
Classification of doubly periodic untwisted (p,q)-weaves by their crossing number and matrices	1
A combinatorial proof of invariance of double-point enhanced grid homology	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
Decomposability of minimal defect branched coverings over the projective plane	1
Left orderability for surgeries on the [1,1,2,2,2j] two-bridge knots	1
Cyclic sets from ribbon string links	1
Properties of minimal charts and their applications VIII: Charts of type (7)	1
Reducible surgery in lens spaces and seiferters	1
Multi-virtual knot theory	1
Symmetry groups of hyperbolic links and their complements	1
A note on Rivin’s interpretation of McShane’s identity as identities for closed geodesics with one self-intersection	1
An improvement of the lower bound for the minimum number of link colorings by quandles	1
Carric mat and the further research on bipartite knots	1
A construction of multiple group racks	1
Author index Volume 32	1
Generalized knots–quivers correspondence	1
Regular projections of the link L6n1	1
Embedding Alexander quandles into groups	1
Region colorings of surfaces in 4-space	1
Alexander and Markov theorems for generalized knots, II generalized braids	1
Finite involutory quandles of two-bridge links with an axis	1
Two-bridge links and stable maps into the plane	1
Link-homotopy classes of 4-component links, claspers and the Habegger–Lin algorithm	1
The one-row-colored ????????3 Jones polynomials for pretzel links	1