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 2020-11-01 to 2024-11-01.)

Article	Citations
Large color R-matrix for knot complements and strange identities	10
Fixing the functoriality of Khovanov homology: A simple approach	6
A diagrammatic approach for determining the braid index of alternating links	6
Parity, virtual closure and minimality of knotoids	5
Polynomial invariants of singular knots and links	5
On multiplying curves in the Kauffman bracket skein algebra of the thickened four-holed sphere	5
Persistent homology for hypergraphs and computational tools — A survey for users	5
On two-bridge knots and a conjecture of Hirasawa–Murasugi	4
Torus knots obtained by negatively twisting torus knots	3
Quandle coloring quivers of (p,2)-torus links	3
Rectangular knot diagrams classification with deep learning	3
Verification of the Jones unknot conjecture up to 24 crossings	3
Classification of doubly periodic untwisted (p,q)-weaves by their crossing number and matrices	3
Weakly reducible H′-splittings of 3-manifolds	3
The second Yang–Baxter homology for the HOMFLYPT polynomial	3
Ribbonlength and crossing number for folded ribbon knots	3
New computations of the superbridge index	3
Kauffman skein algebras and quantum Teichmüller spaces via factorization homology	3
Torsion in Khovanov homology of homologically thin knots	3
Knots with equal bridge index and braid index	3
Goussarov–Polyak–Viro conjecture for degree three case	2
A polyhedral approach to the arithmetic and geometry of hyperbolic link complements	2
Arrow diagrams on spherical curves and computations	2
The non-orientable 4-genus for knots with 10 crossings	2
Peripheral elements in reduced Alexander modules	2

Multivariate Alexander quandles, II. The involutory medial quandle of a link (corrected)	2
Ribbonlength of twisted torus knots	2
Twisted cohomology pairings of knots II; to some Blanchfield pairings	2
A lower bound on critical points of the electric potential of a knot	2
The tightest knot is not necessarily the smallest	2
A diagrammatic presentation and its characterization of non-split compact surfaces in the 3-sphere	2
Quandle coloring quivers of links using dihedral quandles	2
Tied links in the solid torus	2
Singquandles, psyquandles, and singular knots: A survey	2
Big data approaches to knot theory: Understanding the structure of the Jones polynomial	2
From chord parity to chord index	2
Arithmetic Chern–Simons theory with real places	2
Characterizing slopes for torus knots, II	2
Anomaly-free TQFTs from the super Lie algebra ??(2\|1)	2
Homology of relative trisection and its applications	2
Virtual concordance and the generalized Alexander polynomial	2
Multiflypes of rectangular diagrams of links	2
Decompositions of the 3-sphere and lens spaces with three handlebodies	2
Quandle coloring quivers of (p,3)-torus links	2
Determining the doubly slice genera of prime knots with up to 12 crossings	2
Tied links in various topological settings	2
The colored Jones polynomial and Kontsevich–Zagier series for double twist knots	2
All prime knots through 10 crossings have superbridge index ≤ 5	2
On the virtual singular braid monoid	2
Superbridge and bridge indices for knots	2
Diquandles and invariants for oriented dichromatic links	2
An Alexander-type invariant for doodles	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
Legendrian satellites and decomposable cobordisms	2
Determinants of twisted generalized hybrid weaving knots	2
Coefficients of catalan states without nesting and maximal number of returns	2
Polynomial invariants, knot homologies, and higher twist numbers of weaving knots W(3,n)	2
Twist moves and the affine index polynomials of virtual knots	1
Some computations on instanton knot homology	1
Virtual mosaic knot theory	1
Narrowing the gap between combinatorial and hyperbolic knot invariants via deep learning	1
On the potential functions for a link diagram	1
Petal number of torus knots of type (r,r + 2)	1
Describing realizable Gauss diagrams using the concepts of parity or bipartite graphs	1
Group presentations for links in thickened surfaces	1
On the periodic non-orientable 4-genus a knot	1
2-knot homology and Roseman move	1
Capturing links in spatial complete graphs	1
Palettes of Dehn colorings for spatial graphs and the classification of vertex conditions	1
The minimum number of coloring of knots	1
The complement problem for linklessly embeddable graphs	1
The Rohlin invariant and ℤ/2-valued invariants of homology spheres	1
Cohomological invariants of representations of 3-manifold groups	1
On arrow polynomials of checkerboard colorable virtual links	1
Maps on random hypergraphs and random simplicial complexes	1

Symmetric union presentations for 2-bridge ribbon knots	1
Writhe-like invariants of alternating links	1
Khovanov–Lipshitz–Sarkar homotopy type for links in thickened higher genus surfaces	1
Petal number of torus knots using superbridge indices	1
Non-slice 3-stranded pretzel knots	1
Alternating odd pretzel knots and chirally cosmetic surgeries	1
Knot invariants for rail knotoids	1
The reduced Dijkgraaf–Witten invariant of twist knots in the Bloch group of a finite field	1
Linking numbers, quandles and groups	1
Canonical sphere bases for simplicial and cubical complexes	1
Unknotting twisted knots with Gauss diagram forbidden moves	1
B-type Catalan states of lattice crossing	1
Extremal Khovanov homology and the girth of a knot	1
Regular projections of the link L6n1	1
Fundamental heap for framed links and ribbon cocycle invariants	1
The unrestricted virtual braid groups UV Bn	1
3-Manifolds with nilpotent embeddings in S4	1
Parity on based matrices	1
The smooth 4-genus of (the rest of) the prime knots through 12 crossings	1
Structures of homomorphisms induced by arc selection game and arc freeze selection game	1
Alexander and Markov theorems for generalized knots, II generalized braids	1
Vertex distortion of lattice knots	1
A categorification of the Vandermonde determinant	1
Topological symmetry groups of the Petersen graph	1
On universal parity on free two-dimensional knots	1
Parity functors	1
A note on closed 3-braid knot shadows	1
Connected sum of virtual knots and F-polynomials	1
Equivariant annular Khovanov homology	1
Non-hyperbolic solutions to tangle equations involving composite links	1
Lefschetz open book decompositions of 4-manifolds	1
Most graphs are knotted	1
Hyperbolicity of augmented links in the thickened torus	1
Almost all strongly quasipositive braid closures are fibered	1
Biquandle brackets and knotoids	1
On long knots in the full torus	1
Unknotting operations on knots and links	1
Thesaurus racks: Categorizing rack objects	1
Integral geometric orbifolds	1
A Möbius invariant discretization of O’Hara’s Möbius energy	1
The number of oriented rational links with a given deficiency number	1
Virtual multicrossings and petal diagrams for virtual knots and links	1
Periods of continued fractions and volumes of modular knots complements	1
On equivalence of symmetric union presentations for ribbon knots	1
The embedded homology of hypergraph pairs	1
The knot invariant Υ using grid homologies	1
Explicit volume formula for a hyperbolic tetrahedron in terms of edge lengths	1
The disk complex and topologically minimal surfaces in the 3-sphere	1
Virtual index cocycles and invariants of virtual links	1
Bieberbach groups and flat manifolds with finite abelian holonomy from Artin braid groups	1
Personal recollection of Vaughan F. R. Jones (1952–2020)	1