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Main Authors:	Bellettini, Giovanni, Paolini, Giovanni, Paolini, Maurizio, Wang, Yi-Sheng
Format:	Preprint
Published:	2025
Subjects:	Geometric Topology 57K12, 05C10
Online Access:	https://arxiv.org/abs/2511.07796
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On unique decomposition of knotted handlebodies
by: Bellettini, Giovanni, et al.
Published: (2025)

A complete invariant for doodles on a 2-sphere
by: Mostovoy, Jacob
Published: (2024)

Equivalence of Doubly Periodic Tangles
by: Diamantis, Ioannis, et al.
Published: (2023)

Minimal generating sets of moves for diagrams of isotopic knots and spatial trivalent graphs
by: Caprau, Carmen, et al.
Published: (2022)

Minimal crossing diagrams of spatial graphs
by: Flapan, Erica, et al.
Published: (2025)

Mutation, surface graphs, and alternating links in surfaces
by: Boden, Hans U., et al.
Published: (2023)

Multi-Virtual Knot Theory
by: Kauffman, Louis H
Published: (2024)

A categorification for the partial-dual genus polynomial
by: Cheng, Zhiyun, et al.
Published: (2024)

Directional Invariants of Doubly Periodic Tangles
by: Diamantis, Ioannis, et al.
Published: (2024)

The Theory of Doubly Periodic Pseudo Tangles
by: Diamantis, Ioannis, et al.
Published: (2024)

Signature, slicing foams, and crossing changes of Klein graphs
by: Baker, Kenneth L., et al.
Published: (2024)

Stuck Knots: Rigidity, Invariants, and Unsticking Distance
by: Diamantis, Ioannis
Published: (2026)

Construction of weaving and polycatenane motifs from periodic tilings of the plane
by: Fukuda, Mizuki, et al.
Published: (2022)

Loops in surfaces, chord diagrams, interlace graphs: operad factorisations and generating grammars
by: Simon, Christopher-Lloyd
Published: (2023)

A multi-variable Alexander polynomial for a framed transverse graph
by: Bao, Yuanyuan, et al.
Published: (2025)

On symmetry and exterior problems of knotted handlebodies
by: Koda, Yuya, et al.
Published: (2025)

The Cayley graph of a quandle
by: Dolžan, David, et al.
Published: (2026)

Welded graphs, Wirtinger groups and knotted punctured spheres
by: Audoux, Benjamin, et al.
Published: (2023)

Region crossing change on planar trivalent graphs
by: Cheng, Zhiyun
Published: (2022)

A generating set of Reidemeister moves of oriented virtual knots
by: Ali, Danish
Published: (2025)

Classification of virtual links by arc shift move
by: Sahore, Aastha, et al.
Published: (2025)

R-equivalence classes of $\mathrm{Rot} \mathbb{E}^{2}$-colorings of torus knots
by: Sato, Mai
Published: (2025)

A bound on the equivariant unknotting number
by: Zampa, Sarah
Published: (2025)

A construction of multiple group racks
by: Arai, Katsunori
Published: (2025)

Arc shift move and region arc shift move for twisted knots
by: Mahato, Tumpa, et al.
Published: (2026)

Warping labeling for twisted knots and twisted virtual braids
by: Negi, Komal, et al.
Published: (2024)

How essential is a spanning surface?
by: Kindred, Thomas
Published: (2024)

The H(n)-move is an unknotting operation for virtual and welded links
by: Ali, Danish, et al.
Published: (2022)

On the neighborhood of knots
by: Panagiotou, Eleni
Published: (2024)

Coloring invariants for links in $Σ_g\times S^1$
by: Cheng, Zhiyun, et al.
Published: (2024)

A new unknotting operation for classical and welded links
by: Ali, Danish, et al.
Published: (2022)

Connected sum and crossing numbers of flat virtual knots
by: Chen, Jie
Published: (2023)

A note on Fox colorings of virtual tangles
by: Nakamura, Takuji, et al.
Published: (2026)

Orbits by the up-down action of braid diagrams
by: Negi, Komal, et al.
Published: (2024)

Liftings of knots in $S_{g} \times S^{1}$ and covering of virtual knots
by: Kim, Seongjeong
Published: (2023)

The untangling number of 3-periodic tangles
by: Andriamanalina, Toky, et al.
Published: (2025)

Links on incompressible surfaces and volumes
by: Reid, Corbin
Published: (2025)

Explicit formulae for the Aicardi-Juyumaya bracket of tied links
by: Cárdenas-Andaur, O'Bryan, et al.
Published: (2025)

Knot quandle decomposition along a torus
by: Bonatto, Marco, et al.
Published: (2020)

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