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Generalization of knots in 3-dimensional Euclidean space
Likewise a virtual knot can be considered an equivalence of virtual knot diagrams that are equivalent under generalized Reidemeister moves. Virtual knots allow
Virtual_knot
Unique knot with a crossing number of four
In knot theory, a figure-eight knot (also called Listing's knot) is the unique knot with a crossing number of four. This makes it the knot with the third-smallest
Figure-eight knot (mathematics)
Figure-eight_knot_(mathematics)
Simplest non-trivial closed knot with three crossings
In knot theory, a branch of mathematics, the trefoil knot is the simplest example of a nontrivial knot. The trefoil can be obtained by joining the two
Trefoil_knot
Prime knot named for John Horton Conway
In mathematics, specifically in knot theory, the Conway knot (or Conway's knot) is a particular knot with 11 crossings, named after John Horton Conway
Conway_knot
Mathematical theory
physical knots. Drawing a straight line from one end of a curve to another effectively closes it into a loop. After this virtual closure, the knot can be
Open_knot_theory
Study of mathematical knots
In topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope,
Knot_theory
Embedding of the circle in three dimensional Euclidean space
mathematics, a knot is an embedding of the circle (S1) into three-dimensional Euclidean space, R3 (also known as E3). Often two knots are considered equivalent
Knot_(mathematics)
Mathematical knot with crossing number 5
In knot theory, the cinquefoil knot, also known as Solomon's seal knot or the pentafoil knot, is one of two knots with crossing number five, the other
Cinquefoil_knot
Family of mathematical knots
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. (That
Twist_knot
Non-trivial knot which cannot be written as the knot sum of two non-trivial knots
In knot theory, a prime knot or prime link is a knot that is, in a certain sense, indecomposable. Specifically, it is a non-trivial knot which cannot
Prime_knot
Motif with two doubly-interlinked loops
classified as a link, and is not a true knot according to the definitions of mathematical knot theory. The Solomon's knot consists of two closed loops, which
Solomon's_knot
Integer-valued knot invariant; least number of crossings in a knot diagram
mathematical area of knot theory, the crossing number of a knot is the smallest number of crossings of any diagram of the knot. It is a knot invariant. By way
Crossing_number_(knot_theory)
Knot which lies on the surface of a torus in 3-dimensional space
In knot theory, a torus knot is a special kind of knot that lies on the surface of an unknotted torus in R3. Similarly, a torus link is a link which lies
Torus_knot
Mathematical knot with crossing number 7
In knot theory, the 71 knot, also known as the septoil knot, the septafoil knot, or the (7, 2)-torus knot, is one of seven prime knots with crossing number
71_knot
Knot that bounds an embedded disk in 4-space
A slice knot is a mathematical knot in 3-dimensional space that bounds an embedded disk in 4-dimensional space. A knot K ⊂ S 3 {\displaystyle K\subset
Slice_knot
Mathematical knot with crossing number 7
In knot theory, the Pentatwist knot, also known as the five-twist knot, or the 72, is one of seven prime knots with crossing number seven. It is the fifth
7_2_knot
Type of mathematical knot
pretzel knot, sometimes called the Fintushel–Stern knot (after Ron Fintushel and Ronald J. Stern), is an important example of a pretzel knot which exhibits
(−2,3,7)_pretzel_knot
Type of knot in knot theory
Bridge number 2 In the mathematical field of knot theory, a 2-bridge knot is a knot which can be regular isotoped so that the natural height function given
2-bridge_knot
Mathematical knot with crossing number 5
In knot theory, the three-twist knot is the twist knot with three-half twists. It is listed as the 52 knot in the Alexander-Briggs notation, and is one
Three-twist_knot
Polynomials arising in knot theory
field of knot theory, the HOMFLY polynomial or HOMFLYPT polynomial, sometimes called the generalized Jones polynomial, is a 2-variable knot polynomial
HOMFLY_polynomial
Special ordered sets
quandles and racks. In the theory of virtual knots, biquandles are analagous to quandles in the theory of classical knots. Biracks and racks have the same
Biracks_and_biquandles
Collection of knots that do not intersect, but may be linked
mathematical knot theory, a link is a collection of knots that do not intersect, but which may be linked (or knotted) together. A knot can be described
Link_(knot_theory)
Function of a knot that takes the same value for equivalent knots
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. The equivalence
Knot_invariant
of knot theory, a knot polynomial is a knot invariant in the form of a polynomial whose coefficients encode some of the properties of a given knot. The
Knot_polynomial
contact structure. Lissajous knot Ribbon knot Satellite knot Slice knot Torus knot Transverse knot Twist knot Virtual knot Wild knot Borromean rings, the simplest
List_of_knot_theory_topics
Knot that can't be tied in a string of constant diameter
In the mathematical theory of knots, a knot is tame if it can be "thickened", that is, if there exists an extension to an embedding of the solid torus
Wild_knot
Mathematical knot with crossing number 7
In mathematical knot theory, 74 is the name of a 7-crossing knot which can be visually depicted in a highly-symmetric form, and so appears in the symbolism
74_knot
Loop seen as a trivial knot
of knots, the unknot, not knot, or trivial knot, is the least knotted of all knots. Intuitively, the unknot is a closed loop of rope without a knot tied
Unknot
Mathematical knot with crossing number 6
In knot theory, the 62 knot is one of three prime knots with crossing number six, the others being the stevedore knot and the 63 knot. This knot is sometimes
62_knot
Three linked but pairwise separated rings
the "Ballantine rings". The first work of knot theory to include the Borromean rings was a catalog of knots and links compiled in 1876 by Peter Tait.
Borromean_rings
In knot theory, prime knots are those knots that are indecomposable under the operation of knot sum. The prime knots with ten or fewer crossings are listed
List_of_prime_knots
Fundamental group of a knot complement
a knot is an embedding of a circle into 3-dimensional Euclidean space. The knot group of a knot K is defined as the fundamental group of the knot complement
Knot_group
Mathematical knot with crossing number 6
In knot theory, the stevedore knot is one of three prime knots with crossing number six, the others being the 62 knot and the 63 knot. The stevedore knot
Stevedore_knot_(mathematics)
Invariant of mathematical knots
abutting to their instanton knot Floer homology group and used this to show that Khovanov Homology (like the instanton knot Floer homology) detects the
Khovanov_homology
Notation used to describe knots based on operations on tangles
In knot theory, Conway notation, invented by John Horton Conway, is a way of describing knots that makes many of their properties clear. It composes a
Conway_notation_(knot_theory)
Type of mathematical knot
mathematical theory of knots, a satellite knot is a knot that contains an incompressible, non boundary-parallel torus in its complement. Every knot is either hyperbolic
Satellite_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
Alternating_knot
Knot that is not equivalent to its mirror image
field of knot theory, a chiral knot is a knot that is not equivalent to its mirror image (when identical while reversed). An oriented knot that is equivalent
Chiral_knot
Connected sum of two trefoil knots with opposite chirality
In knot theory, the square knot is a composite knot obtained by taking the connected sum of a trefoil knot with its reflection. It is closely related
Square_knot_(mathematics)
Attempt to classify and tabulate all possible knots
tabulate all possible knots. By 1998, all 1.7 million prime knots up to 16 crossings had been tabulated, and by 2020 all 350 million knots up to 19 crossings
Knot_tabulation
Orientable surface whose boundary is a knot or link
boundary is a given knot or link. Such surfaces can be used to study the properties of the associated knot or link. For example, many knot invariants are most
Seifert_surface
Mathematical invariant of a knot or link
of knot theory, the Jones polynomial is a knot polynomial discovered by Vaughan Jones in 1984. Specifically, it is an invariant of an oriented knot or
Jones_polynomial
Group whose operation is a composition of braids
§ Introduction). Example applications of braid groups include knot theory, where any knot may be represented as the closure of certain braids (a result
Braid_group
Knot invariant
a knot invariant which assigns a polynomial with integer coefficients to each knot type. James Waddell Alexander II discovered this, the first knot polynomial
Alexander_polynomial
Mathematical knot with crossing number 6
In knot theory, the 63 knot is one of three prime knots with crossing number six, the others being the stevedore knot and the 62 knot. It is alternating
63_knot
Encyclopedic website dedicated to knot theory
The Knot Atlas is a website, an encyclopedia rather than atlas, dedicated to knot theory. It and its predecessor were created by mathematician Dror Bar-Natan
The_Knot_Atlas
Connected sum of two trefoil knots with same chirality
In knot theory, the granny knot is a composite knot obtained by taking the connected sum of two identical trefoil knots. It is closely related to the square
Granny_knot_(mathematics)
Type of mathematical link
knot (the figure-eight knot) 52 knot (the three-twist knot) 61 knot (the stevedore knot) 62 knot 63 knot 74 knot 10 161 knot (the "Perko pair" knot)
Hyperbolic_link
American mathematician (born 1989)
is primarily known for having solved Gromov's problem on distortion of knots, for which he received the 2012 Morgan Prize. He is a permanent member of
John_Pardon
Type of invariant in Knot theory
mathematical theory of knots, a finite type invariant, or Vassiliev invariant (so named after Victor Anatolyevich Vassiliev), is a knot invariant that can
Finite_type_invariant
Peter Guthrie Tait in his study of knots. The Tait conjectures involve concepts in knot theory such as alternating knots, chirality, and writhe. All of the
Tait_conjectures
Two interlinked loops with five structural crossings
In knot theory, the Whitehead link, named for J. H. C. Whitehead, is one of the most basic links. It can be drawn as an alternating link with five crossings
Whitehead_link
as knot theory, an invertible knot is a knot that can be continuously deformed to itself, but with its orientation reversed. A non-invertible knot is
Invertible_knot
Simplest nontrivial knot link
In mathematical knot theory, the Hopf link is the simplest nontrivial link with more than one component. It consists of two circles linked together exactly
Hopf_link
mathematical knots and links. See also list of knots, list of geometric topology topics. 01 knot/Unknot - a simple un-knotted closed loop 31 knot/Trefoil knot -
List of mathematical knots and links
List_of_mathematical_knots_and_links
Prime knot with crossing number 10
theory of knots, the Perko pair, named after Kenneth Perko, is a pair of entries in classical knot tables that actually represent the same knot. In Dale
Perko_pair
Topological quantum field theory
"A spinning construction for virtual 1-knots and 2-knots, and the fiberwise and welded equivalence of virtual 1-knots". arXiv:1808.03023 [math.GT]. Kauffman
Chern–Simons_theory
Property in knot theory
In the mathematical field of knot theory, the tricolorability of a knot is the ability of a knot to be colored with three colors subject to certain rules
Tricolorability
Complement of a knot in three-sphere
In mathematics, the knot complement of a tame knot K is the space where the knot is not. If a knot is embedded in the 3-sphere, then the complement is
Knot_complement
Knot invariant named after Cahit Arf
In the mathematical field of knot theory, the Arf invariant of a knot, named after Cahit Arf, is a knot invariant obtained from a quadratic form associated
Arf_invariant_of_a_knot
Minimum number of times a specific knot must be passed through itself to become untied
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
Unknotting_number
Link that consists of finitely many unlinked unknots
unlink in Wiktionary, the free dictionary. In the mathematical field of knot theory, an unlink is a link that is equivalent (under ambient isotopy) to
Unlink
In knot theory, a knot move or operation is a change or changes which preserve crossing number. Operations are used to investigate whether knots are equivalent
Knot_operation
Normalized hyperbolic volume of the complement of a hyperbolic knot
In the mathematical field of knot theory, the hyperbolic volume of a hyperbolic link is the volume of the link's complement with respect to its complete
Hyperbolic_volume
Mathematical notation for describing the structure of knots
In the mathematical field of knot theory, the Dowker–Thistlethwaite (DT) notation or code, for a knot diagram is a sequence of even integers. The notation
Dowker–Thistlethwaite notation
Dowker–Thistlethwaite_notation
Polynomial invariant of framed links
In the mathematical field of knot theory, the bracket polynomial (also known as the Kauffman bracket) is a polynomial invariant of framed links. Although
Bracket_polynomial
functions (Hao Huang, 2019) Deciding whether the Conway knot is a slice knot (Lisa Piccirillo, 2020) Virtual Haken conjecture (Ian Agol, Daniel Groves, Jason
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Type of mathematical knot
In the mathematical area of knot theory, a ribbon knot is a knot that bounds a self-intersecting disk with only ribbon singularities. Intuitively, this
Ribbon_knot
Andean record-keeping system using knotted cords
Cusco Quechua: khipu, [kʰipu]), are record-keeping devices fashioned from knotted cords. They were historically used by various cultures in the central Andes
Quipu
Invariant of framed knots
In knot theory, the self-linking number is an invariant of framed knots. It is related to the linking number of curves. A framing of a knot is a choice
Self-linking_number
Every knot or link can be represented as a closed braid
In mathematics Alexander's theorem states that every knot or link can be represented as a closed braid; that is, a braid in which the corresponding ends
Alexander's_theorem
Mathematical tool for studying knots
tool used to study knots. A central question in the mathematical theory of knots is whether two knot diagrams represent the same knot. One way to answer
Skein_relation
Class of mathematical knot with special properties
theory of knots, a Berge knot (named after mathematician John Berge) or doubly primitive knot is any member of a particular family of knots in the 3-sphere
Berge_knot
Mathematical knot
In knot theory, a branch of mathematics, a knot or link K {\displaystyle K} in the 3-dimensional sphere S 3 {\displaystyle S^{3}} is called fibered or
Fibered_knot
Invariant of a knot diagram
In knot theory, there are several competing notions of the quantity writhe, or Wr {\displaystyle \operatorname {Wr} } . In one sense, it is purely a property
Writhe
Non-orientable surface with one edge
Sazdanović, Radmila (2011). "Nonplanar graphs derived from Gauss codes of virtual knots and links". Journal of Mathematical Chemistry. 49 (10): 2250–2267. doi:10
Möbius_strip
Two-variable polynomial knot invariant
In knot theory, the Kauffman polynomial is a 2-variable knot polynomial due to Louis Kauffman. It is initially defined on a link diagram as F ( K ) (
Kauffman_polynomial
Determining whether a knot is the unknot
algorithmically recognizing the unknot, given some representation of a knot, e.g., a knot diagram. There are several types of unknotting algorithms. A major
Unknotting_problem
One of three types of isotopy-preserving local changes to a knot diagram
In the mathematical area of knot theory, a Reidemeister move is any of three local moves on a link diagram. Kurt Reidemeister (1927) and, independently
Reidemeister_move
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
Bridge_number
Analog of the knot group
In knot theory, an area of mathematics, the link group of a link is an analog of the knot group of a knot. They were described by John Milnor in his Ph
Link_group
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
Tunnel_number
Serbian mathematician and crystallographer
of colored symmetry (2007) Knot theory: Nonplanar graphs derived from Gauss codes of virtual knots and links (2011) Knots in art (2012) Delta diagrams
Slavik_Vlado_Jablan
In the mathematical field of knot theory, the crosscap number of a knot K is the minimum of C ( K ) ≡ 1 − χ ( S ) , {\displaystyle C(K)\equiv 1-\chi (S)
Crosscap_number
Smallest number of edges of an equivalent polygonal path for a knot
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. Specifically
Stick_number
How many times curves wind around each other
the form of the linking integral. It is an important object of study in knot theory, algebraic topology, and differential geometry, and has numerous applications
Linking_number
Flat woven decorative knot
The carrick mat is a flat woven decorative knot which can be used as a mat or pad. Its name is based on the mat's decorative-type carrick bend with the
Carrick_mat
Interlinked multi-loop construction where cutting one loop frees all the others
In knot theory, a branch of topology, a Brunnian link is a nontrivial link that becomes a set of trivial unlinked circles if any one component is removed
Brunnian_link
Link formed from a finite number of twisted sections
In the mathematical theory of knots, a pretzel link is a special kind of link. It consists of a finite number of tangles made of two intertwined circular
Pretzel_link
Device or point within a network capable of creating, receiving, or transmitting data
In networking, a node (Latin: nodus, 'knot') is either a redistribution point or a communication endpoint within telecommunication networks or computer
Node_(networking)
Thoroughbred racehorse
2009-10-6 "Hall of Fame Tie the Knot". racingvictoria.com.aun. Retrieved 17 May 2021. "Tie The Knot Dies Aged 18". Virtual Formguide. Archived from the original
Tie_the_Knot
Kind of operation in knot theory
field of knot theory, a mutation is an operation on a knot that can produce different knots. Suppose K is a knot given in the form of a knot diagram.
Mutation_(knot_theory)
Concept in knot theory
In mathematical knot theory, a Conway sphere, named after John Horton Conway, is a 2-sphere intersecting a given knot or link in a 3-manifold transversely
Conway_sphere
Operation on a knot
of knots, a flype is a kind of manipulation of knot and link diagrams used in the Tait flyping conjecture. It consists of twisting a part of a knot, a
Flype
Link of three loops with ten crossings
In the mathematical theory of knots, L10a140 is the name in the Thistlethwaite link table of a link of three loops, which has ten crossings between the
L10a140_link
"Cherries and Flowers" March 13, 2017 (2017-03-13) N/A Chelsea and Cole tie the knot. Kailyn and Javi try to make amends. Leah prepares for a new chapter in her
List_of_Teen_Mom_2_episodes
Russian news website
Caucasian Knot (Russian: Кавказский узел, romanized: Kavkazkii Uzel) is an online news site that covers the Caucasus region in English and Russian. It
Caucasian_Knot
American mathematician
Her dissertation, A Sequence of Degree One Vassiliev Invariants for Virtual Knots, was supervised by Vladimir Chernov. At Dartmouth, Carolyn S. Gordon
Allison_Henrich
Proteins with backbone entangled in a knot
the knots discovered in proteins are deep trefoil (31) knots. Figure eight knots (41), three-twist knots (52), Stevedore knots (61) and Septoil knot (71)
Knotted_protein
American saxophonist (born 1989)
Records) Joe Gilman – Americanvas (Capri Records) Hironori Momoi – Liquid Knots (Independent) "Chad LB – SFCM". sfcm.edu. "How jazz great Arturo O'Farrill
Chad_Lefkowitz-Brown
VIRTUAL KNOT
VIRTUAL KNOT
Boy/Male
Hindu
Priceless, Precious
Girl/Female
Australian, Jamaican
Virtuous; Strength
Surname or Lastname
English and Scottish
English and Scottish : nickname from Middle English, Old French vertu ‘moral worth’; ‘goodness’ (Latin virtus ‘manliness’, ‘valor’, ‘worth’). This may have been bestowed on a good or pious person, it may alternatively have been a sarcastic nickname for a prig, or it may have been borne by someone who had played the part of Virtue in a medieval mystery play.
Boy/Male
Indian
Name of Lord Krishna
Boy/Male
Hindu
Lively
Girl/Female
Indian
Virtues
Girl/Female
Latin
Virtue.
Boy/Male
Sikh
Heroic protector, Protector of the brave
Boy/Male
Indian, Punjabi, Sikh
Protector of the Brave
Boy/Male
Tamil
Virtues
Boy/Male
Indian
Feeling, Virtual
Girl/Female
Hindu
Lord Vishnu, Fortune giver
Boy/Male
Hindu
Lord Vishnu, Fortune giver
Boy/Male
British, English, French, German, Latin
Lively
Girl/Female
Gujarati, Hindu, Indian, Kannada
Bravery
Boy/Male
Hindu, Indian, Marathi
Extensive; King
Boy/Male
Indian, Modern
Incomparable
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi
Lord Vishnu
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit
Priceless; Natural; Deep Thinker
Boy/Male
Tamil
Feeling, Virtual
VIRTUAL KNOT
VIRTUAL KNOT
VIRTUAL KNOT
VIRTUAL KNOT
VIRTUAL KNOT
VIRTUAL KNOT
VIRTUAL KNOT