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 2021-02-01 to 2025-02-01.)

Article	Citations
Homflypt skein theory, string topology and 2-categories	6
Welded extensions and ribbon restrictions of diagrammatical moves	6
A polyhedral approach to the arithmetic and geometry of hyperbolic link complements	5
Linking in tree-manifolds	5
The action of the Kauffman bracket skein algebra of the torus on the Kauffman bracket skein module of the 3-twist knot complement	4
Non-hyperbolic solutions to tangle equations involving composite links	3
The reduced Dijkgraaf–Witten invariant of twist knots in the Bloch group of a finite field	3
Garside groups and geometry: Some thoughts for Patrick Dehornoy	3
A numerical invariant of oriented links	3
A short remembrance of Vaughan	3
The Gordian complex of theta-curves	3
On inequalities between unknotting numbers and crossing numbers of spatial embeddings of trivializable graphs and handlebody-knots	3
4-Move distance of knots	3
A short proof of a theorem of Tanaka on composite knots with symmetric union presentations	3
Remembering Patrick Dehornoy	3
3-Bridgeness under adding crossings to alternating 3-bridge knots in a 3-bridge representation	2
Bounds in simple hexagonal lattice and classification of 11-stick knots	2
Spatial graph as connected sum of a planar graph and a braid	2
Petal number of torus knots using superbridge indices	2
Combinatorial knot theory and the Jones polynomial	2
Distinguishing surface-links described by 4-charts with two crossings and eight black vertices	2
Erratum: Decompositions of the 3-sphere and lens spaces with three handlebodies	2
Self-dual maps III: Projective links	2
Doodles and commutator identities	2
Braids for unoriented Pretzel links	2

Some congruence of the generalized Alexander invariant for periodic virtual links	2
Twist moves and the affine index polynomials of virtual knots	2
Minimal generating sets of moves for surfaces immersed in the four-space	2
On classification of genus g knots which admit a (1,1)-decomposition	2
Integral left-orderable surgeries on genus one fibered knots	2
On hyperelliptic Euclidean 3-manifolds	2
Bieberbach groups and flat manifolds with finite abelian holonomy from Artin braid groups	2
All prime knots through 10 crossings have superbridge index ≤ 5	2
Satellite constructions and geometric classification of Brunnian links	2
A note on closed 3-braid knot shadows	2
On alternating closed braids	2
Reducible surgery in lens spaces and seiferters	2
Good involutions of generalized Alexander quandles	2
Derivatives of Jones polynomials detect delta moves in virtual knots	2
Quandle coloring quivers of (p,q)-torus links	2
A note on the involutive invariants of certain pretzel knots	2
Concordance invariant Υ for balanced spatial graphs using grid homology	2
More 1-cocycles for classical knots	2
A new Garside structure on torus knot groups and some complex braid groups	2
Alternating odd pretzel knots and chirally cosmetic surgeries	2
Vertex distortion detects the unknot	2
The homological arrow polynomial for virtual links	2
On the 3-loop polynomial of genus 1 knots with trivial Alexander polynomial	2
Twisted virtual bikeigebras and twisted virtual handlebody-knots	2
The stick number of rail arcs	1
Knot quandle decomposition along a torus	1
Limits of the Tristram–Levine signature function	1
Connected sum and crossing numbers of flat virtual knots	1
Almost all 2-bridge knots are curly	1
Explicit volume formula for a hyperbolic tetrahedron in terms of edge lengths	1
Classification of links up to one-two-way pass-move	1
Embedding Alexander quandles into groups	1
A categorification of the Vandermonde determinant	1
Connected sum of virtual knots and F-polynomials	1
HOMFLYPT homology over ℤ2 detects unlinks	1
The colored Jones polynomial and Kontsevich–Zagier series for double twist knots	1
A free-group valued invariant of free knots	1
Cable knots obtained by positively twisting torus knots	1
A combinatorial description of the LOSS Legendrian knot invariant	1
Twisted Alexander invariants for the braid group associated with the Tong–Yang–Ma representation	1
Tied links in various topological settings	1
Special Issue in Memory of Patrick Dehornoy	1
A prime decomposition theorem for string links in a thickened surface	1
Khovanov–Lipshitz–Sarkar homotopy type for links in thickened higher genus surfaces	1
The non-orientable 4-genus of 11 crossing non-alternating knots	1
A diagrammatic approach for determining the braid index of alternating links	1
Tangles in affine Hecke algebras	1
On the geometry of two state models for the colored Jones polynomial	1
New superbridge index calculations from non-minimal realizations	1
Symmetric union presentations for 2-bridge ribbon knots	1

A bracket polynomial for virtual links	1
Octahedral developing of knot complement II: Ptolemy coordinates and applications	1
Vaughan Jones at IHES	1
Peripheral elements in reduced Alexander modules: An addendum	1
Memories of Vaughan from his student days and after	1
H(2)-moves on torus links of type (2,2n)	1
Anomaly-free TQFTs from the super Lie algebra ????????(2\|1)	1
Identifying non-pseudo-alternating knots by using the free factor property of minimal genus Seifert surfaces	1
The computational complexity of classical knot recognition	1
Quotients of the Gordian and H(2)-Gordian graphs	1
Arithmetic Chern–Simons theory with real places	1
Alexander and Markov theorems for generalized knots, II generalized braids	1
On the uniqueness of Sarkar-Seed-Szabo construction	1
A spinning construction for virtual 1-knots and 2-knots, and the fiberwise and welded equivalence of virtual 1-knots	1
Ordering braids: In memory of Patrick Dehornoy	1
Cyclic coverings of the 3-sphere branched over wild knots of dynamically defined type	1
Infinitely many arithmetic alternating links: Class number greater than one	1
Legendrian negative torus knots in universally tight lens spaces	1
One more proof of Vassiliev’s conjecture	1
The braid indices of pretzel links: A comprehensive study, Part I	1
Superbridge and bridge indices for knots	1
The Ma–Qiu index and the Nakanishi index for a fibered knot are equal, and ω-solvability	1
Virtual index cocycles and invariants of virtual links	1
Singquandles, psyquandles, and singular knots: A survey	1
Lescop invariants of both the Brieskorn–Hamm manifolds and 3-manifolds obtained by Dehn surgeries on knots	1
Goussarov–Polyak–Viro conjecture for degree three case	1
On universal parity on free two-dimensional knots	1
Group object quandles and their endomorphism nearrings	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
Distinguishing some genus one knots using finite quotients	1
Annular Khovanov homology and meridional disks	1
The non-orientable 4-genus for knots with 10 crossings	1
Bikei module invariants of unoriented surface-links	1
Region crossing change, bicolored diagram and Arf invariant	1
Shrinking braids and left distributive monoid	1
A class of index polynomial invariants for virtual knots using flat virtual knots invariants	1
Big data approaches to knot theory: Understanding the structure of the Jones polynomial	1