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 2020-05-01 to 2024-05-01.)

Article	Citations
Large color R-matrix for knot complements and strange identities	10
Gordian complexes of knots and virtual knots given by region crossing changes and arc shift moves	6
A note on representations of welded braid groups	6
F-polynomials of tabulated virtual knots	5
Some remarks on twin groups	5
Polynomial invariants of singular knots and links	5
Fixing the functoriality of Khovanov homology: A simple approach	5
On Bennequin-type inequalities for links in tight contact 3-manifolds	4
Generalized torsion elements and hyperbolic links	4
On two-bridge knots and a conjecture of Hirasawa–Murasugi	4
Persistent homology for hypergraphs and computational tools — A survey for users	4
On multiplying curves in the Kauffman bracket skein algebra of the thickened four-holed sphere	4
A diagrammatic approach for determining the braid index of alternating links	4
Twisted spectral correspondence and torus knots	3
The second Yang–Baxter homology for the HOMFLYPT polynomial	3
Verification of the Jones unknot conjecture up to 24 crossings	3
Kauffman skein algebras and quantum Teichmüller spaces via factorization homology	3
Twisted torus knots T(p,q,p − kq,−1) which are torus knots	3
A multiple group rack and oriented spatial surfaces	3
Ribbonlength and crossing number for folded ribbon knots	3
Torus knots obtained by negatively twisting torus knots	3
Parity, virtual closure and minimality of knotoids	3
Knots with equal bridge index and braid index	3
On fertility of knot shadows	3
Cuspidal edges with the same first fundamental forms along a knot	2

Tied links in the solid torus	2
The colored Jones polynomial and Kontsevich–Zagier series for double twist knots	2
Diquandles and invariants for oriented dichromatic links	2
The non-orientable 4-genus for knots with 10 crossings	2
??n-webs, categorification and Khovanov–Rozansky homologies	2
Multivariate Alexander quandles, II. The involutory medial quandle of a link (corrected)	2
A description of Rasmussen’s invariant from the divisibility of Lee’s canonical class	2
Interior polynomial for signed bipartite graphs and the HOMFLY polynomial	2
Multiflypes of rectangular diagrams of links	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
Weakly reducible H′-splittings of 3-manifolds	2
Rectangular knot diagrams classification with deep learning	2
Tied links in various topological settings	2
Genera of knots in the complex projective plane	2
Torsion calculations in Khovanov cohomology	2
Superbridge and bridge indices for knots	2
New computations of the superbridge index	2
String-net models for nonspherical pivotal fusion categories	2
Real algebraic links in S3 and braid group actions on the set of n-adic integers	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
Determining the doubly slice genera of prime knots with up to 12 crossings	2
Polynomial invariants, knot homologies, and higher twist numbers of weaving knots W(3,n)	2
Big data approaches to knot theory: Understanding the structure of the Jones polynomial	2
Tau invariants for balanced spatial graphs	2
An Alexander-type invariant for doodles	2
All prime knots through 10 crossings have superbridge index ≤ 5	2
Multistring based matrices	2
Presentation of a ribbon 2-knot	2
Twisted cohomology pairings of knots II; to some Blanchfield pairings	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
Determinants of twisted generalized hybrid weaving knots	2
Some remarks on the chord index	2
From chord parity to chord index	1
Arithmetic Chern–Simons theory with real places	1
The complement problem for linklessly embeddable graphs	1
Arrow diagrams on spherical curves and computations	1
A polyhedral approach to the arithmetic and geometry of hyperbolic link complements	1
3-Manifolds with nilpotent embeddings in S4	1
Writhe-like invariants of alternating links	1
The reduced Dijkgraaf–Witten invariant of twist knots in the Bloch group of a finite field	1
On equivalence of symmetric union presentations for ribbon knots	1
Suciu’s ribbon 2-knots with isomorphic group	1
On the periodic non-orientable 4-genus a knot	1
Non-slice 3-stranded pretzel knots	1
Fundamental heap for framed links and ribbon cocycle invariants	1
Palettes of Dehn colorings for spatial graphs and the classification of vertex conditions	1
Refined large N duality for knots	1

Knotting probability of an arc diagram	1
Personal recollection of Vaughan F. R. Jones (1952–2020)	1
Refined Chern–Simons theory in genus two	1
Linking numbers, quandles and groups	1
The knot invariant Υ using grid homologies	1
On the potential functions for a link diagram	1
Homology of relative trisection and its applications	1
A categorification of the Vandermonde determinant	1
On long knots in the full torus	1
Topological symmetry groups of the Petersen graph	1
Twist moves and the affine index polynomials of virtual knots	1
Thesaurus racks: Categorizing rack objects	1
The minimum number of coloring of knots	1
Petal number of torus knots using superbridge indices	1
Peripheral elements in reduced Alexander modules	1
Bieberbach groups and flat manifolds with finite abelian holonomy from Artin braid groups	1
Black holes and topological surgery	1
On the lower central series of some virtual knot groups	1
Anomaly-free TQFTs from the super Lie algebra ??(2\|1)	1
The number of oriented rational links with a given deficiency number	1
Cohomological invariants of representations of 3-manifold groups	1
Non-hyperbolic solutions to tangle equations involving composite links	1
Legendrian satellites and decomposable cobordisms	1
Narrowing the gap between combinatorial and hyperbolic knot invariants via deep learning	1
Petal number of torus knots of type (r,r + 2)	1
Integral geometric orbifolds	1
Biquandle brackets and knotoids	1
Parity on based matrices	1
Crossing change on Khovanov homology and a categorified Vassiliev skein relation	1
Positive knots and weak (1, 3) homotopy	1
Quandle coloring quivers of links using dihedral quandles	1
Knot invariants for rail knotoids	1
On arrow polynomials of checkerboard colorable virtual links	1
Minimal grid diagrams of 11 crossing prime alternating knots	1
Maps on random hypergraphs and random simplicial complexes	1
Quandle coloring quivers of (p,2)-torus links	1
The smooth 4-genus of (the rest of) the prime knots through 12 crossings	1
Explicit volume formula for a hyperbolic tetrahedron in terms of edge lengths	1
Shake slice and shake concordant links	1
Ribbonlength of twisted torus knots	1
Goussarov–Polyak–Viro conjecture for degree three case	1
Vertex distortion of lattice knots	1
Connected sum of virtual knots and F-polynomials	1
Structures of homomorphisms induced by arc selection game and arc freeze selection game	1
A Möbius invariant discretization of O’Hara’s Möbius energy	1
Virtual mosaic knot theory	1
Capturing links in spatial complete graphs	1
The disk complex and topologically minimal surfaces in the 3-sphere	1
Alternating odd pretzel knots and chirally cosmetic surgeries	1
The structure of biquandle brackets	1
Prime alternating knots of minimal warping degree two	1
Most graphs are knotted	1
Extending quasi-alternating links	1
Extremal Khovanov homology and the girth of a knot	1
Almost all strongly quasipositive braid closures are fibered	1
Restrictions on Homflypt and Kauffman polynomials arising from local moves	1
An infinite family of braid group representations in automorphism groups of free groups	1
Coefficients of catalan states without nesting and maximal number of returns	1
The Rohlin invariant and ℤ/2-valued invariants of homology spheres	1
Virtual concordance and the generalized Alexander polynomial	1
The embedded homology of hypergraph pairs	1
Unknotting twisted knots with Gauss diagram forbidden moves	1
Classification of doubly periodic untwisted (p,q)-weaves by their crossing number and matrices	1
The special rank of virtual knot groups	1
Hyperbolicity of augmented links in the thickened torus	1
Periods of continued fractions and volumes of modular knots complements	1
Equivariant annular Khovanov homology	1
On the virtual singular braid monoid	1
Edge-preserving maps of the nonseparating curve graphs, curve graphs and rectangle preserving maps of the Hatcher–Thurston graphs	1
Canonical sphere bases for simplicial and cubical complexes	1
On knot groups acting on trees	1
Singquandles, psyquandles, and singular knots: A survey	1