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
Linking in tree-manifolds	5
Connected sum and crossing numbers of flat virtual knots	5
New superbridge index calculations from non-minimal realizations	4
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
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
Quandle action quivers	2
Gauss diagram formulae for Vassiliev invariants from Kauffman polynomial	2
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
Intersecting subgroups and symmetric commutator subgroups in virtual link groups	2
Forty years in mathematics: Personal perspective (Part I)	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
Invariants of spatial graphs coming from maximal trees	2
A groupoid rack and spatial surfaces	2
Some experimental results on knots and links constructed from elements of Thompson’s group F à la Jones	2
Matrix representation for some generalized braid-like groups	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
A note on Murasugi sum of trivially extendable relative trisections	2
On the geometry and bounded cohomology of racks and quandles	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
Embedding Alexander quandles into groups	1
Finite involutory quandles of two-bridge links with an axis	1
The one-row-colored ????????3 Jones polynomials for pretzel links	1
Alexander and Markov theorems for generalized knots, II generalized braids	1
Positive braids minimize ascending number	1
Two-bridge links and stable maps into the plane	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
Memories of Vaughan from his student days and after	1
Tri-plane diagrams for simple surfaces in S4	1
Jones rational coincidences	1
Trisection embeddings of non-orientable 4-manifolds	1
An algorithm to calculate generalized Seifert matrices	1
The Jones polynomials of three-bridge knots via Chebyshev knots and billiard table diagrams	1
Some polynomial invariants of virtual doodles	1
Linking number for graph-links and some classification of graph-links	1
On homogeneous quasipositive links	1
Invariants of annular links, cobordisms and transverse links from combinatorial link Floer complex	1
Signed heights of knotoids	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
Trisections induced by the Gluck surgery along certain spun knots	1
The H(n)-move is an unknotting operation for virtual and welded links	1

A universal algebraic approach to rack coverings	1
Origins of the Temperley-Lieb Algebra: Early History	1
Regular isotopy classes of link diagrams from Thompson’s groups	1
Colorings of Symmetric Unions and Partial Knots	1
Representations of flat virtual braids which do not preserve the forbidden relations	1
Orbits by the up–down action of braid diagrams	1
B-type Catalan states of lattice crossing	1
A Torres-type formula for the Alexander polynomial of spatial graphs	1
Families of curly knots	1
Garside groups and geometry: Some thoughts for Patrick Dehornoy	1
Special Issue in Memory of Patrick Dehornoy	1
Relationship of the Hennings and Witten–Reshetikhan–Turaev invariants for higher rank quantum groups	1
Some generalizations of Satoh’s Tube map	1
The special shadow-complexity of #k(S1 × S3)	1
Counting the number of connected components of multi-curves through corresponding permutations	1
In Memory of Vaughan Jones (Renzo L. Ricca)	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
Shade quandle presentations for oriented links	1
Knot cobordism and Lee’s perturbation of Khovanov homology	1
Octahedral developing of knot complement II: Ptolemy coordinates and applications	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
Computations of HOMFLY homology	1
On the braid index of a two-bridge knot	1
On the swap move of letters in words and the forbidden moves in virtual diagrams	1
Fibered 3-manifolds with unique incompressible surfaces	1
A combinatorial proof of invariance of double-point enhanced grid homology	1
On pretzel links which are concordant to the trivial link	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
Simple braids tend toward positive entropy	1
Left orderability for surgeries on the [1,1,2,2,2j] two-bridge knots	1
Classification of doubly periodic untwisted (p,q)-weaves by their crossing number and matrices	1
Decomposability of minimal defect branched coverings over the projective plane	1
Properties of minimal charts and their applications VIII: Charts of type (7)	1
Multi-virtual knot theory	1
Cyclic sets from ribbon string links	1
Symmetry groups of hyperbolic links and their complements	1
An improvement of the lower bound for the minimum number of link colorings by quandles	1
Reducible surgery in lens spaces and seiferters	1
Author index Volume 32	1
A note on Rivin’s interpretation of McShane’s identity as identities for closed geodesics with one self-intersection	1
Carric mat and the further research on bipartite knots	1
Regular projections of the link L6n1	1
A construction of multiple group racks	1
Generalized knots–quivers correspondence	1
Region colorings of surfaces in 4-space	1