# Questions tagged [knot-theory]

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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### Is there a combinatorial way to determine the coefficients of the universal finite-type invariant on a given knot?

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### Notation for algebraic tangles

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### The Kirby diagram of a manifold glued along the lens space $L(p,1)$

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### From braid representations to link invariants

**13**

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### Which knots appear as the singular locus of a polyhedral metric on the 3-sphere?

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### Computation of Colored HOMFLY Polynomials

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### Rack cohomology as derived functor cohomology

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### Braids of fibered knots

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### Thompson's group F and algebraic links

**6**

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### Decidability of knot equivalence in general 3-manifolds? Surface equivalence?

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### What is the determinant of the R-matrix defining the colored Jones polynomial?

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### Questions on the proof Lemma 4.5 GTM 175, Lickorish

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### Rolling wheel unicycle knots

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### Are knot invariants topological invariants? [closed]

**2**

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### Skein relation, Braids, and Hecke algebra

**1**

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### Questions about a few terminologies in “Knots and Links” by Rolfsen

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### Distinguishable knots (with constraints) over polyhedra

**2**

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### Surveys on unknotting number

**7**

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### Can the Chern-Simons invariant of a cusped hyperbolic $3$-manfiold be defined mod $\mathbb Z$?

**3**

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### Knots with a braid presentation with only positive or negative crossings on each fixed position

**12**

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### Several questions about Gauss's mathematical conception of braids

**4**

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### Does a periodic and strongly invertible knot have a specific type of diagram?

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### Knot theory and creative writing

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### Invariants of virtual knots?

**3**

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### Handle decompositions of slice and ribbon disk exteriors

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### (Best) ways to reduce knot complexity?

**4**

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### Mazur homology spheres

**5**

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### Two knots with same Dowker-Thistlethwaite code have isomorphic knot groups?

**3**

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### $0$-surgery of slice knots and contractible manifolds

**5**

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### Actions of two types of Kauffman skein categories

**5**

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### Exchanging the components of a two-component link

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### Possible “binomial” formula for the Jones polynomial

**3**

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### Unknotting in Morse notation without introducing new strands

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### Would it be simpler, pedagogically speaking, if textbook writers introduced root systems as an example of a quandle?

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### Using a 4th dimension to make Seifert surfaces isotopic?

**6**

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### Singularities of PL embedding of surface in a contractible 4-manifold

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### Knots realized as algebraic curves

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### Assigning a “canonical geometry” to a Seifert surface

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### Bipartedly slice links and their surgeries

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### Maximal Thurston--Bennequin number of boundary knot classes in contact handlebodies

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### references on categorification of knot invariants

**7**

**2**answers

### What are the “correct” references for the Vassiliev invariant?

**3**

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### Is every tricolourable knot chiral?

**11**

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### $0$-surgeries on trefoil and figure-eight

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### JSJ-type decompositions for knots

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### Harmonic functions on knot complements

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### May this slice disk for the unknot be pushed into the boundary?

**7**

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### Rational slice knot that is not slice

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### unlinking when relaxing the homeomorphism condition

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