Knot theory is dealing with embedding of curves in manifolds of dimension 3. A knot is a single circle embedded in the affine space of dimension 3 as a smooth curve not crossing itself. Many knot invariants are known and can be used to distinguish knots.

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### Framing dependence of HOMFLY polynomial

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### Quandle homomorphism does not always induces group homomorphism on inner automorphism groups of quandles

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### Blow-up and Blow-down kirby local moves for non-orientable $3$-manifold

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### Multivariate Alexander polynomial vs single variable (Conway) Alexander polynomial

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### How are characterstic polynomials (resp. Alexander polynomials) distributed amongst adjacency matrices (resp. grid diagrams)?

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### Define the 3d Chern-Simons TQFT on a discrete simplicial complex

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### Is the Lisca-Matic bound (aka slice-Bennequin bound) strictly stronger than the Bennequin bound?

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### “Flat links”, a reference request

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### Multivariable vs single variable Alexander polynomial for links?

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### Why should I care about the Jones polynomial?

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### What is an ambient isotopy categorically?

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### What is the complexity of determining if a knot group is $\mathbb{Z}$?

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### Knots of fixed genus with arbitrarily large volume

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### Maximum possible crossing number of a restricted tangle family

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### Show a sequence of sums involving Catalan Numbers converges

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### How disconnected can a Seifert surface be?

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### Links defined by link-severance tableau

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### Theory of Irrational Tangles?

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### Tying knots via gravity-assisted spaceship trajectories

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### Isotopy extension theorem: how non-unique is ambient isotopy

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### How to add essentially new knots to the universe?

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### Why are two diffeomorphims of $R^n$ are always homotopic (in the same category)?

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### Conformal boundary and cusp of figure-8 complement

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### Knot Factorization Homology inputs

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### Presentations of the monoidal categories of virtual tangles and of welded tangles by generators and relations

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### Link such that deleting any two components leaves an unlink

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### Resolving a mismatch in indexing conventions of knot/link Floer homologies

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### Tangled random triangles: One giant component?

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### Can we compute the Tristram–Levine signatures of a knot in $S^3$ using Jacobian with Fox partial derivatives?

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### Interactions between pseudoline arrangements and braid groups?

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### Does annular Khovanov homology detect the unknot (in annulus)?

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### Version of Khovanov homology that does not produce torsion?

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### Generating prime knots (in order)

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### Slicing satellite knots

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### Factor traces of the Temperley-Lieb algebra

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### Minimum required crossings in a link diagram for a $k$-component Brunnian link

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### Infinitely many Brunnian links with bounded crossings

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### How many non-homeomorphic collections of $N$ circles in $\mathbb{R}^3$ are there?

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### How hard is it to guess Kuperberg's certificate of knottedness?

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### Can we cut and rotate a particular region of a hyperbolic 3-manifold to get another (non-homeomorphic) hyperbolic 3-manifold?

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### What does it mean exactly for a pair of $S^0$'s to be unlinked on a knot $K$?

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### Can a knot be cables of two different knots?

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### Classifying links with essential annuli in the complement as torus links

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### Fary-Milnor Theorem : Help following a proof on page 9

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### Does Lackenby's polynomial bound on knot moves imply polynomial mixing in “Quantum Money From Knots?”

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### Can a planar tangle have an infinite number of input disks?

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### Lutz twist and open book decompositions

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### Can knot non-equivalence be a proof-of-work for a cryptocurrency?

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### Pull-back of knots in branched covers and the Alexander polynomial

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