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 2021-06-01 to 2025-06-01.)

Article	Citations
Twisted Alexander invariants for the braid group associated with the Tong–Yang–Ma representation	7
A note on the involutive invariants of certain pretzel knots	7
The non-orientable 4-genus of 11 crossing non-alternating knots	6
Self-dual maps III: Projective links	6
Connected sum and crossing numbers of flat virtual knots	5
A Spectrum Connecting the Bridge Index and the Braid Index	4
New superbridge index calculations from non-minimal realizations	4
Linking in tree-manifolds	4
Virtual index cocycles and invariants of virtual links	4
Limits of the Tristram–Levine signature function	4
Vertex distortion detects the unknot	4
A combinatorial description of the LOSS Legendrian knot invariant	3
A visit in Valparaíso	3
Embedding Tangles in Links and Gaussian Integers	3
Integral geometric orbifolds	3
Multivariate Alexander quandles, IV. The medial quandle of a link	3
A multivariable polynomial invariant of virtual knots	3
A polynomial invariant of Kauffman type for knotoids	2
Knots with properties of a trefoil knot concerning unknotting operations	2
Forty years in mathematics: Personal perspective (Part I)	2
A diagrammatic presentation and its characterization of non-split compact surfaces in the 3-sphere	2
The F-polynomial invariant for knotoids	2
Gauss diagram formulae for Vassiliev invariants from Kauffman polynomial	2
Quandle action quivers	2
On the geometry and bounded cohomology of racks and quandles	2

Memories of Vaughan Jones	2
Preface for Special Issue for Vaughan Jones	2
Local-moves on knots and products of knots II	2
A new invariant of planar knotoids and finite-type invariants	2
Extremal Khovanov homology and the girth of a knot	2
A groupoid rack and spatial surfaces	2
Preface	2
The Rohlin invariant and ℤ/2-valued invariants of homology spheres	2
Conversion to almost classical virtual links and pseudo Goeritz matrices	2
Heegaard presentations and Milnor pairings of some knots	2
Embedding tangles and the Kauffman bracket polynomials	2
Invariants of spatial graphs coming from maximal trees	2
Quantum invariants of links and 3-manifolds with boundary defined via virtual links	2
Bi-Legendrian rack colorings of Legendrian knots	2
Algebra, topology and the discoveries of Vaughan Jones	2
A note on Murasugi sum of trivially extendable relative trisections	2
On Some New Oriented Singquandles And Their Shadows	2
One conjecture on cut points of virtual links and the arrow polynomial of twisted links	2
Remembering Vaughan Jones	2
On annulus presentations, dualizable patterns and RGB-diagrams	2
On linear resolvability of universal quantum dimensions	2
Group-valued invariant of knots in the full torus	2
Generalization of arc shift for twisted knots	2
Erratum: Milnor’s triple linking number and Gauss diagram formulas of 3-bouquet graphs	2
Pentagon equations, Delaunay triangulations and pure braid group invariant	2
Regular isotopy classes of link diagrams from Thompson’s groups	2
Intersecting subgroups and symmetric commutator subgroups in virtual link groups	2
Classification of doubly periodic untwisted (p,q)-weaves by their crossing number and matrices	1
Personal recollection of Vaughan F. R. Jones (1952–2020)	1
Invariants of annular links, cobordisms and transverse links from combinatorial link Floer complex	1
Regular projections of the link L6n1	1
A note on Rivin’s interpretation of McShane’s identity as identities for closed geodesics with one self-intersection	1
Region crossing change on origami and link	1
Garside groups and geometry: Some thoughts for Patrick Dehornoy	1
A new framework for the Jones polynomial of fluid knots	1
On hyperelliptic Euclidean 3-manifolds	1
A complete list of minimal diagrams of an oriented alternating knot	1
A Torres-type formula for the Alexander polynomial of spatial graphs	1
The one-row-colored ????????3 Jones polynomials for pretzel links	1
On homogeneous quasipositive links	1
Fibered 3-manifolds with unique incompressible surfaces	1
Representations of flat virtual braids which do not preserve the forbidden relations	1
Coefficients of catalan states without nesting and maximal number of returns	1
Two-bridge links and stable maps into the plane	1
Symmetry groups of hyperbolic links and their complements	1
Reducible surgery in lens spaces and seiferters	1
In Memory of Vaughan Jones (Renzo L. Ricca)	1
Embedding Alexander quandles into groups	1
Tri-plane diagrams for simple surfaces in S4	1
Trisections induced by the Gluck surgery along certain spun knots	1

B-type Catalan states of lattice crossing	1
Biquandle brackets and knotoids	1
Counting the number of connected components of multi-curves through corresponding permutations	1
The special shadow-complexity of #k(S1 × S3)	1
On invariants of surfaces in the 3-sphere	1
Multivariate Alexander quandles, V. Constructing the medial quandle of a link	1
Lefschetz open book decompositions of 4-manifolds	1
Cyclic sets from ribbon string links	1
My memories of Vaughan Jones	1
Connected sum of virtual knots and F-polynomials	1
Linking number for graph-links and some classification of graph-links	1
Octahedral developing of knot complement II: Ptolemy coordinates and applications	1
A class of index polynomial invariants for virtual knots using flat virtual knots invariants	1
Crossing numbers and rotation numbers of cycles in a plane immersed graph	1
Special Issue in Memory of Patrick Dehornoy	1
Some generalizations of Satoh’s Tube map	1
On pretzel links which are concordant to the trivial link	1
Author index Volume 32	1
Left orderability for surgeries on the [1,1,2,2,2j] two-bridge knots	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
Alexander and Markov theorems for generalized knots, II generalized braids	1
The Jones polynomials of three-bridge knots via Chebyshev knots and billiard table diagrams	1
An algorithm to calculate generalized Seifert matrices	1
A Seifert algorithm for integral homology spheres	1
Knot cobordism and Lee’s perturbation of Khovanov homology	1
On the swap move of letters in words and the forbidden moves in virtual diagrams	1
Shade quandle presentations for oriented links	1
Characterizing slopes for torus knots, II	1
Twisted cohomology pairings of knots II; to some Blanchfield pairings	1
Some polynomial invariants of virtual doodles	1
The photography method: Solving pentagon equation	1
Memories of Vaughan from his student days and after	1
Enhanced index polynomials for virtual knots	1
The H(n)-move is an unknotting operation for virtual and welded links	1
Polynomial and signature invariants for pseudo-links via Goeritz matrices	1
Carric mat and the further research on bipatite knots	1
From integrals to combinatorial formulas of finite type invariants — A case study	1
Simple braids tend toward positive entropy	1
Periods of continued fractions and volumes of modular knots complements	1
Finite involutory quandles of two-bridge links with an axis	1
On the braid index of a two-bridge knot	1
Properties of minimal charts and their applications VIII: Charts of type (7)	1
Jones rational coincidences	1
Families of curly knots	1
Link-homotopy classes of 4-component links, claspers and the Habegger–Lin algorithm	1
Orbits by the up–down action of braid diagrams	1
Relationship of the Hennings and Witten–Reshetikhan–Turaev invariants for higher rank quantum groups	1
Multi-virtual knot theory	1
The intersection polynomials of a virtual knot IV: Crossing change and supporting genus	1
A universal algebraic approach to rack coverings	1
An improvement of the lower bound for the minimum number of link colorings by quandles	1
Signed heights of knotoids	1