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Finite type invariant

Index Finite type invariant

In the mathematical theory of knots, a finite type invariant, or Vassiliev invariant, is a knot invariant that can be extended (in a precise manner to be described) to an invariant of certain singular knots that vanishes on singular knots with m + 1 singularities and does not vanish on some singular knot with 'm' singularities. [1]

17 relations: Algebra over a field, American Mathematical Society, Arf invariant of a knot, Immersion (mathematics), Inventiones Mathematicae, Joan Birman, Knot invariant, Knot theory, Kontsevich invariant, Link (knot theory), Link group, Maxim Kontsevich, Mutation (knot theory), Oleg Viro, Victor Anatolyevich Vassiliev, Willerton's fish, 3-manifold.

Algebra over a field

In mathematics, an algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product.

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American Mathematical Society

The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.

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Arf invariant of a knot

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 to a Seifert surface.

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Immersion (mathematics)

In mathematics, an immersion is a differentiable function between differentiable manifolds whose derivative is everywhere injective.

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Inventiones Mathematicae

Inventiones Mathematicae is a mathematical journal published monthly by Springer Science+Business Media.

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Joan Birman

Joan Sylvia Lyttle Birman (born May 30, 1927 in New York CityLarry Riddle. "", Biographies of Women Mathematicians, at Agnes Scott College) is an American mathematician, specializing in braid theory and knot theory.

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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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Kontsevich invariant

In the mathematical theory of knots, the Kontsevich invariant, also known as the Kontsevich integral of an oriented framed link, is a universal Vassiliev invariant in the sense that any coefficient of the Kontsevich invariant is of a finite type, and conversely any finite type invariant can be presented as a linear combination of such coefficients.

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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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Link group

In knot theory, an area of mathematics, the link group of a link is an analog of the knot group of a knot.

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Maxim Kontsevich

Maxim Lvovich Kontsevich (Макси́м Льво́вич Конце́вич;; born 25 August 1964) is a Russian and French mathematician.

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Mutation (knot theory)

In the mathematical field of knot theory, a mutation is an operation on a knot that can produce different knots.

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Oleg Viro

Oleg Yanovich Viro (Олег Янович Виро) (b. 13 May 1948, Leningrad, USSR) is a Russian mathematician in the fields of topology and algebraic geometry, most notably real algebraic geometry, tropical geometry and knot theory.

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Victor Anatolyevich Vassiliev

Victor Anatolyevich Vassiliev or Vasilyev (Виктор Анатольевич Васильев; born April 10, 1956), is a Soviet and Russian mathematician.

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Willerton's fish

In knot theory, Willerton's fish is an unexplained relationship between the first two Vassiliev invariants of a knot.

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3-manifold

In mathematics, a 3-manifold is a space that locally looks like Euclidean 3-dimensional space.

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Redirects here:

Goussarov-Vassiliev invariant, Vassiliev invariant, Vassiliev knot invariant, Vassiliev-Goussarov invariant.

References

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

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