Table of Contents
26 relations: Alternating knot, Average crossing number, Bridge number, Conjecture, DNA, Figure-eight knot (mathematics), Gel electrophoresis, Knot (mathematics), Knot invariant, Knot theory, Linking number, Marc Lackenby, Mathematical proof, Mathematics, Normal surface, Open problem, Peter Guthrie Tait, Prime knot, Satellite knot, Stick number, Torus knot, Trefoil knot, Twist knot, Unknot, Unknotting number, 0.
- Knot invariants
Alternating knot
In knot theory, a knot or link diagram is alternating if the crossings alternate under, over, under, over, as one travels along each component of the link. Crossing number (knot theory) and alternating knot are knot invariants.
See Crossing number (knot theory) and Alternating knot
Average crossing number
In the mathematical subject of knot theory, the average crossing number of a knot is the result of averaging over all directions the number of crossings in a knot diagram of the knot obtained by projection onto the plane orthogonal to the direction.
See Crossing number (knot theory) and Average crossing number
Bridge number
In the mathematical field of knot theory, the bridge number, also called the bridge index, is an invariant of a knot defined as the minimal number of bridges required in all the possible bridge representations of a knot. Crossing number (knot theory) and bridge number are knot invariants.
See Crossing number (knot theory) and Bridge number
Conjecture
In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof.
See Crossing number (knot theory) and Conjecture
DNA
Deoxyribonucleic acid (DNA) is a polymer composed of two polynucleotide chains that coil around each other to form a double helix.
See Crossing number (knot theory) and DNA
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 Crossing number (knot theory) and Figure-eight knot (mathematics)
Gel electrophoresis
Gel electrophoresis is a method for separation and analysis of biomacromolecules (DNA, RNA, proteins, etc.) and their fragments, based on their size and charge.
See Crossing number (knot theory) and Gel electrophoresis
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 Crossing number (knot theory) 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. Crossing number (knot theory) and knot invariant are knot invariants.
See Crossing number (knot theory) and Knot invariant
Knot theory
In topology, knot theory is the study of mathematical knots.
See Crossing number (knot theory) and Knot theory
Linking number
In mathematics, the linking number is a numerical invariant that describes the linking of two closed curves in three-dimensional space. Crossing number (knot theory) and linking number are knot invariants.
See Crossing number (knot theory) and Linking number
Marc Lackenby
Marc Lackenby is a professor of mathematics at the University of Oxford whose research concerns knot theory, low-dimensional topology, and group theory.
See Crossing number (knot theory) and Marc Lackenby
Mathematical proof
A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion.
See Crossing number (knot theory) and Mathematical proof
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.
See Crossing number (knot theory) and Mathematics
Normal surface
In mathematics, a normal surface is a surface inside a triangulated 3-manifold that intersects each tetrahedron in several components called normal disks. Each normal disk is either a triangle which cuts off a vertex of the tetrahedron, or a quadrilateral which separates pairs of vertices.
See Crossing number (knot theory) and Normal surface
Open problem
In science and mathematics, an open problem or an open question is a known problem which can be accurately stated, and which is assumed to have an objective and verifiable solution, but which has not yet been solved (i.e., no solution for it is known).
See Crossing number (knot theory) and Open problem
Peter Guthrie Tait
Peter Guthrie Tait (28 April 18314 July 1901) was a Scottish mathematical physicist and early pioneer in thermodynamics.
See Crossing number (knot theory) and Peter Guthrie Tait
Prime knot
In knot theory, a prime knot or prime link is a knot that is, in a certain sense, indecomposable. Crossing number (knot theory) and prime knot are knot invariants.
See Crossing number (knot theory) and Prime knot
Satellite knot
In the mathematical theory of knots, a satellite knot is a knot that contains an incompressible, non boundary-parallel torus in its complement.
See Crossing number (knot theory) and Satellite knot
Stick number
In the mathematical theory of knots, the stick number is a knot invariant that intuitively gives the smallest number of straight "sticks" stuck end to end needed to form a knot. Crossing number (knot theory) and stick number are knot invariants.
See Crossing number (knot theory) and Stick number
Torus knot
In knot theory, a torus knot is a special kind of knot that lies on the surface of an unknotted torus in R3.
See Crossing number (knot theory) and Torus knot
Trefoil knot
In knot theory, a branch of mathematics, the trefoil knot is the simplest example of a nontrivial knot.
See Crossing number (knot theory) and Trefoil knot
Twist knot
In knot theory, a branch of mathematics, a twist knot is a knot obtained by repeatedly twisting a closed loop and then linking the ends together.
See Crossing number (knot theory) and Twist knot
Unknot
In the mathematical theory of knots, the unknot, not knot, or trivial knot, is the least knotted of all knots.
See Crossing number (knot theory) and Unknot
Unknotting number
In the mathematical area of knot theory, the unknotting number of a knot is the minimum number of times the knot must be passed through itself (crossing switch) to untie it. Crossing number (knot theory) and unknotting number are knot invariants.
See Crossing number (knot theory) and Unknotting number
0
0 (zero) is a number representing an empty quantity.
See Crossing number (knot theory) and 0
See also
Knot invariants
- Alexander polynomial
- Alternating knot
- Arf invariant of a knot
- Bridge number
- Crosscap number
- Crossing number (knot theory)
- Finite type invariant
- Hyperbolic volume
- Jones polynomial
- Khovanov homology
- Knot chirality
- Knot group
- Knot invariant
- Knot polynomial
- Kontsevich invariant
- Link concordance
- Link group
- Linking number
- Prime knot
- Ropelength
- Self-linking number
- Signature of a knot
- Stick number
- Thurston–Bennequin number
- Tricolorability
- Tunnel number
- Unknotting number