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Invertible knot

In mathematics, especially in the area of topology known as knot theory, an invertible knot is a knot that can be continuously deformed to itself, but with its orientation reversed. ^[1]

19 relations: Almost all, Ambient isotopy, Chiral knot, Conway notation (knot theory), Crossing number (knot theory), Figure-eight knot (mathematics), Hale Trotter, Involution (mathematics), Knot (mathematics), Knot invariant, Knot theory, Link (knot theory), Mathematics, On-Line Encyclopedia of Integer Sequences, Pretzel link, Ralph Fox, Topology, Trefoil knot, Tunnel number.
Invertible knots and links

Almost all

In mathematics, the term "almost all" means "all but a negligible quantity".

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In the mathematical subject of topology, an ambient isotopy, also called an h-isotopy, is a kind of continuous distortion of an ambient space, for example a manifold, taking a submanifold to another submanifold.

See Invertible knot and Ambient isotopy

Chiral knot

In the mathematical field of knot theory, a chiral knot is a knot that is not equivalent to its mirror image (when identical while reversed).

See Invertible knot and Chiral knot

Conway notation (knot theory)

In knot theory, Conway notation, invented by John Horton Conway, is a way of describing knots that makes many of their properties clear.

See Invertible knot and Conway notation (knot theory)

Crossing number (knot theory)

In the mathematical area of knot theory, the crossing number of a knot is the smallest number of crossings of any diagram of the knot.

See Invertible knot and Crossing number (knot theory)

Figure-eight knot (mathematics)

In knot theory, a figure-eight knot (also called Listing's knot) is the unique knot with a crossing number of four.

See Invertible knot and Figure-eight knot (mathematics)

Hale Trotter

Hale Freeman Trotter (30 May 1931 – 17 January 2022)biographical information from American Men and Women of Science, Thomson Gale 2004 was a Canadian-American mathematician, known for the Lie–Trotter product formula, the Steinhaus–Johnson–Trotter algorithm, and the Lang–Trotter conjecture.

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Involution (mathematics)

In mathematics, an involution, involutory function, or self-inverse function is a function that is its own inverse, for all in the domain of.

See Invertible knot and Involution (mathematics)

Knot (mathematics)

In mathematics, a knot is an embedding of the circle into three-dimensional Euclidean space, (also known as). Often two knots are considered equivalent if they are ambient isotopic, that is, if there exists a continuous deformation of which takes one knot to the other.

See Invertible knot and Knot (mathematics)

Knot invariant

In the mathematical field of knot theory, a knot invariant is a quantity (in a broad sense) defined for each knot which is the same for equivalent knots.

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Knot theory

In topology, knot theory is the study of mathematical knots.

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Link (knot theory)

In mathematical knot theory, a link is a collection of knots which do not intersect, but which may be linked (or knotted) together.

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Mathematics

Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.

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On-Line Encyclopedia of Integer Sequences

The On-Line Encyclopedia of Integer Sequences (OEIS) is an online database of integer sequences.

See Invertible knot and On-Line Encyclopedia of Integer Sequences

Pretzel link

In the mathematical theory of knots, a pretzel link is a special kind of link.

See Invertible knot and Pretzel link

Ralph Fox

Ralph Hartzler Fox (March 24, 1913 – December 23, 1973) was an American mathematician.

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Topology

Topology (from the Greek words, and) is the branch of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself.

See Invertible knot and Topology

Trefoil knot

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

See Invertible knot and Trefoil knot

Tunnel number

In mathematics, the tunnel number of a knot, as first defined by Bradd Clark, is a knot invariant, given by the minimal number of arcs (called tunnels) that must be added to the knot so that the complement becomes a handlebody.

See Invertible knot and Tunnel number

References

[1] https://en.wikipedia.org/wiki/Invertible_knot

Also known as Invertibility (knot theory), Invertible (knot theory), Invertible link, Non-invertible knot, Strongly invertible knot.

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