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 2020-03-01 to 2024-03-01.)

Article	Citations
Large color R-matrix for knot complements and strange identities	9
A neural network approach to predicting and computing knot invariants	6
A note on representations of welded braid groups	6
Gordian complexes of knots and virtual knots given by region crossing changes and arc shift moves	6
Fixing the functoriality of Khovanov homology: A simple approach	5
F-polynomials of tabulated virtual knots	5
Some remarks on twin groups	5
Polynomial invariants of singular knots and links	5
On Bennequin-type inequalities for links in tight contact 3-manifolds	4
Persistent homology for hypergraphs and computational tools — A survey for users	4
Knots with exactly 10 sticks	4
A diagrammatic approach for determining the braid index of alternating links	4
Generalized torsion elements and hyperbolic links	4
Twisted spectral correspondence and torus knots	3
Parity, virtual closure and minimality of knotoids	3
Ribbonlength and crossing number for folded ribbon knots	3
Torus knots obtained by negatively twisting torus knots	3
Twisted torus knots T(p,q,p − kq,−1) which are torus knots	3
The second Yang–Baxter homology for the HOMFLYPT polynomial	3
A multiple group rack and oriented spatial surfaces	3
Kauffman skein algebras and quantum Teichmüller spaces via factorization homology	3
Comparing nonorientable three genus and nonorientable four genus of torus knots	3
Knots with equal bridge index and braid index	3
On fertility of knot shadows	3
??n-webs, categorification and Khovanov–Rozansky homologies	2

Genera of knots in the complex projective plane	2
New computations of the superbridge index	2
Interior polynomial for signed bipartite graphs and the HOMFLY polynomial	2
DNA origami and unknotted A-trails in torus graphs	2
Decompositions of the 3-sphere and lens spaces with three handlebodies	2
Torsion in Khovanov homology of homologically thin knots	2
On realizabilty of Gauss diagrams and constructions of meanders	2
Variational formulae and estimates of O’Hara’s knot energies	2
Tied links in the solid torus	2
All prime knots through 10 crossings have superbridge index ≤ 5	2
Superbridge and bridge indices for knots	2
An Alexander-type invariant for doodles	2
Multistring based matrices	2
Presentation of a ribbon 2-knot	2
Twisted torus knots T(mn + m + 1,mn + 1,mn + m + 2,−1) and T(n + 1,n,2n − 1,−1) are torus knots	2
Braid index bounds ropelength from below	2
Some remarks on the chord index	2
Determining the doubly slice genera of prime knots with up to 12 crossings	2
Rectangular knot diagrams classification with deep learning	2
Tied links in various topological settings	2
The non-orientable 4-genus for knots with 10 crossings	2
Multivariate Alexander quandles, II. The involutory medial quandle of a link (corrected)	2
String-net models for nonspherical pivotal fusion categories	2
A description of Rasmussen’s invariant from the divisibility of Lee’s canonical class	2
Multivariate Alexander quandles, I. The module sequence of a link	2
A lower bound on critical points of the electric potential of a knot	2
A diagrammatic presentation and its characterization of non-split compact surfaces in the 3-sphere	2
On two-bridge knots and a conjecture of Hirasawa–Murasugi	2
Ozsváth-Szabó d-invariants of almost simple linear graphs	2
Verification of the Jones unknot conjecture up to 24 crossings	2
Tau invariants for balanced spatial graphs	2
Functoriality of Khovanov homology	2
Raising crosscap number while lowering unknotting number	1
Fundamental heap for framed links and ribbon cocycle invariants	1
The Rohlin invariant and ℤ/2-valued invariants of homology spheres	1
Extremal Khovanov homology and the girth of a knot	1
Coefficients of catalan states without nesting and maximal number of returns	1
Biquandle brackets and knotoids	1
Cuspidal edges with the same first fundamental forms along a knot	1
The embedded homology of hypergraph pairs	1
Refined large N duality for knots	1
Polynomial invariants, knot homologies, and higher twist numbers of weaving knots W(3,n)	1
Linking numbers, quandles and groups	1
Diquandles and invariants for oriented dichromatic links	1
A categorification of the Vandermonde determinant	1
Ribbonlength of twisted torus knots	1
Non-hyperbolic solutions to tangle equations involving composite links	1
On the potential functions for a link diagram	1
The smooth 4-genus of (the rest of) the prime knots through 12 crossings	1
Goussarov–Polyak–Viro conjecture for degree three case	1

Shake slice and shake concordant links	1
From chord parity to chord index	1
The colored Jones polynomial and Kontsevich–Zagier series for double twist knots	1
Thesaurus racks: Categorizing rack objects	1
Peripheral elements in reduced Alexander modules	1
Big data approaches to knot theory: Understanding the structure of the Jones polynomial	1
3-Manifolds with nilpotent embeddings in S4	1
Arrow diagrams on spherical curves and computations	1
Virtual mosaic knot theory	1
On equivalence of symmetric union presentations for ribbon knots	1
Writhe-like invariants of alternating links	1
Most graphs are knotted	1
Weakly reducible H′-splittings of 3-manifolds	1
Palettes of Dehn colorings for spatial graphs and the classification of vertex conditions	1
Torsion calculations in Khovanov cohomology	1
Mapping class group representations from Drinfeld doubles of finite groups	1
Knotting probability of an arc diagram	1
Non-slice 3-stranded pretzel knots	1
State sum invariants for flat virtual links from the chord index	1
Equivariant annular Khovanov homology	1
Restrictions on Homflypt and Kauffman polynomials arising from local moves	1
Refined Chern–Simons theory in genus two	1
Positive knots and weak (1, 3) homotopy	1
Modified Turaev-Viro invariants from quantum ??(2\|1)	1
On arrow polynomials of checkerboard colorable virtual links	1
On the virtual singular braid monoid	1
Explicit volume formula for a hyperbolic tetrahedron in terms of edge lengths	1
Minimal grid diagrams of 11 crossing prime alternating knots	1
A Möbius invariant discretization of O’Hara’s Möbius energy	1
A polyhedral approach to the arithmetic and geometry of hyperbolic link complements	1
Quandle coloring quivers of (p,2)-torus links	1
Cohomological invariants of representations of 3-manifold groups	1
Singquandles, psyquandles, and singular knots: A survey	1
Canonical sphere bases for simplicial and cubical complexes	1
The knot invariant Υ using grid homologies	1
Knot-theoretic flocks	1
Black holes and topological surgery	1
On knot groups acting on trees	1
Arithmetic Chern–Simons theory with real places	1
The number of oriented rational links with a given deficiency number	1
The disk complex and topologically minimal surfaces in the 3-sphere	1
The reduced Dijkgraaf–Witten invariant of twist knots in the Bloch group of a finite field	1
Legendrian satellites and decomposable cobordisms	1
Suciu’s ribbon 2-knots with isomorphic group	1
Anomaly-free TQFTs from the super Lie algebra ??(2\|1)	1
Extending quasi-alternating links	1
Crossing change on Khovanov homology and a categorified Vassiliev skein relation	1
Prime alternating knots of minimal warping degree two	1
Parity on based matrices	1
Twisted cohomology pairings of knots II; to some Blanchfield pairings	1
Integral geometric orbifolds	1
Quandle coloring quivers of links using dihedral quandles	1
Multiflypes of rectangular diagrams of links	1
On multiplying curves in the Kauffman bracket skein algebra of the thickened four-holed sphere	1
The knot Floer cube of resolutions and the composition product	1
Virtual concordance and the generalized Alexander polynomial	1
Homology of relative trisection and its applications	1
The special rank of virtual knot groups	1
The minimum number of coloring of knots	1
Edge-preserving maps of the nonseparating curve graphs, curve graphs and rectangle preserving maps of the Hatcher–Thurston graphs	1
Hyperbolicity of augmented links in the thickened torus	1
On the lower central series of some virtual knot groups	1
Twist moves and the affine index polynomials of virtual knots	1
On long knots in the full torus	1
Vertex distortion of lattice knots	1
Bieberbach groups and flat manifolds with finite abelian holonomy from Artin braid groups	1
Determinants of twisted generalized hybrid weaving knots	1
Maps on random hypergraphs and random simplicial complexes	1
Connected sum of virtual knots and F-polynomials	1
Capturing links in spatial complete graphs	1
Topological symmetry groups of the Petersen graph	1
Alternating odd pretzel knots and chirally cosmetic surgeries	1
The structure of biquandle brackets	1
Integral metaplectic modular categories	1
Multivariate Alexander quandles, II. The involutory medial quandle of a link	1
Multivariate Alexander quandles, II. The involutory medial quandle of a link	1