mathematics, the Arf invariant of a nonsingular quadratic form over a field of characteristic 2 was defined by Turkish mathematician Cahit Arf (1941) when...

have Arf–Kervaire invariant equal to 0, or half have Arf–Kervaire invariant 0 and the other half have Arf–Kervaire invariant 1. The Kervaire invariant problem...

Cahit Arf (Turkish: [dʒaːhit aɾf]; 24 October 1910 – 26 December 1997) was a Turkish mathematician. He is known for the Arf invariant of a quadratic form...

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...

requires the construction of a knot invariant that distinguishes the trefoil from the unknot. The simplest such invariant is tricolorability: the trefoil...

ribosylation factor, a small GTP-binding protein The Arf invariant in mathematics Argon fluoride laser or ArF laser Atomic Resonance Filter or atomic line filter...

{1}}6} . where Arf ⁡ ( M , Σ ) {\displaystyle \operatorname {Arf} (M,\Sigma )} is the Arf invariant of a certain quadratic form on H 1 ( Σ , Z / 2 Z ) {\displaystyle...

isotopic either topologically or smoothly in the 4-ball. Crosscap number Arf invariant of a knot Murasugi sum Slice genus Seifert, H. (1934). "Über das Geschlecht...

is an invariant of order two. Modulo two, it is equal to the Arf invariant. Any coefficient of the Kontsevich invariant is a finite type invariant. The...

a particular knot is the unknot was a major driving force behind knot invariants, since it was thought this approach would possibly give an efficient algorithm...

distinguished using a knot invariant, a "quantity" which is the same when computed from different descriptions of a knot. Important invariants include knot polynomials...

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...

generalized Jones polynomial, is a 2-variable knot polynomial, i.e. a knot invariant in the form of a polynomial of variables m and l. A central question in...

singly even dimension (4k+2), the L-groups detect the Arf invariant (topologically the Kervaire invariant). The symmetric L-groups of the integers are: L 4...

In the mathematical field of knot theory, a knot polynomial is a knot invariant in the form of a polynomial whose coefficients encode some of the properties...

quaternion groups. The corresponding quadratic form (see below) has Arf invariant 1. The central product of n extraspecial groups of order 8, an even...

Figure-eight knot Common name Figure-eight knot Arf invariant 1 Braid length 4 Braid no. 3 Bridge no. 2 Crosscap no. 2 Crossing no. 4 Genus 1 Hyperbolic...

Gromov–Witten invariant Arf invariant Hopf invariant Invariant theory Framed knot Chern–Simons theory Algebraic geometry Seifert surface Geometric invariant theory...

polynomial discovered by Vaughan Jones in 1984. Specifically, it is an invariant of an oriented knot or link which assigns to each oriented knot or link...

three colors subject to certain rules. Tricolorability is an isotopy invariant, and hence can be used to distinguish between two different (non-isotopic)...

component of 5G technologies. Mathematician Cahit Arf is known for Hasse–Arf theorem and Arf invariant. Physician Hulusi Behçet discovered Behçet's disease...

{\displaystyle =\Delta (-1)} ) is a square number. The signature is an invariant of concordance classes and the signature of slice knots is zero. Furthermore...

(42 1) Invariants Alternating Arf invariant Bridge no. 2-bridge Brunnian Chirality Invertible Crosscap no. Crossing no. Finite type invariant Hyperbolic...

One way to answer the question is using knot polynomials, which are invariants of the knot. If two diagrams have different polynomials, they represent...

by Little in 1900 that the writhe of a reduced diagram of a knot is an invariant (see Tait conjectures), as the two diagrams for the pair have different...

smallest number of crossings of any diagram of the knot. It is a knot invariant. By way of example, the unknot has crossing number zero, the trefoil knot...

are just called quadratic forms. The Arf invariant of a nonsingular quadratic form over F2 is an F2-valued invariant with important applications in both...

In mathematics, the linking number is a numerical invariant that describes the linking of two closed curves in three-dimensional space. Intuitively, the...

a quadratic form in characteristic 2 is of interest related to the Arf invariant – Irving Kaplansky (1974), Linear Algebra and Geometry, p. 27. The bilinear...

are used. The number of colorings meeting these conditions is a knot invariant, independent of the diagram chosen for the link. A trivial link with three...