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Knot group and Torus knot

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Knot group and Torus knot

Knot group vs. Torus knot

In mathematics, a knot is an embedding of a circle into 3-dimensional Euclidean space. In knot theory, a torus knot is a special kind of knot that lies on the surface of an unknotted torus in R3.

Similarities between Knot group and Torus knot

Knot group and Torus knot have 6 things in common (in Unionpedia): Braid group, Euclidean space, Knot (mathematics), Presentation of a group, Trefoil knot, Unknot.

Braid group

In mathematics, the braid group on strands (denoted), also known as the Artin braid group, is the group whose elements are equivalence classes of n-braids (e.g. under ambient isotopy), and whose group operation is composition of braids (see). Example applications of braid groups include knot theory, where any knot may be represented as the closure of certain braids (a result known as Alexander's theorem); in mathematical physics where Artin's canonical presentation of the braid group corresponds to the Yang–Baxter equation (see); and in monodromy invariants of algebraic geometry.

Braid group and Knot group · Braid group and Torus knot · See more »

Euclidean space

In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.

Euclidean space and Knot group · Euclidean space and Torus knot · See more »

Knot (mathematics)

In mathematics, a knot is an embedding of a circle S^1 in 3-dimensional Euclidean space, R3 (also known as E3), considered up to continuous deformations (isotopies).

Knot (mathematics) and Knot group · Knot (mathematics) and Torus knot · See more »

Presentation of a group

In mathematics, one method of defining a group is by a presentation.

Knot group and Presentation of a group · Presentation of a group and Torus knot · See more »

Trefoil knot

In topology, a branch of mathematics, the trefoil knot is the simplest example of a nontrivial knot.

Knot group and Trefoil knot · Torus knot and Trefoil knot · See more »

Unknot

The unknot arises in the mathematical theory of knots.

Knot group and Unknot · Torus knot and Unknot · See more »

The list above answers the following questions

Knot group and Torus knot Comparison

Knot group has 24 relations, while Torus knot has 43. As they have in common 6, the Jaccard index is 8.96% = 6 / (24 + 43).

References

This article shows the relationship between Knot group and Torus knot. To access each article from which the information was extracted, please visit:

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