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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 in characteristic 2 (applied in knot theory and surgery theory ) in topology , the Hasse–Arf theorem in ramification theory , Arf semigroups and Arf rings .
Arf and a formula for the Arf invariant appear on the reverse side of the 2009 Turkish 10 lira note. In mathematics, the Arf invariant of a nonsingular quadratic form over a field of characteristic 2 was defined by Turkish mathematician Cahit Arf () when he started the systematic study of quadratic forms over arbitrary fields of characteristic 2.
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. If F is a Seifert surface of a knot, then the homology group H 1 ( F , Z /2 Z ) has a quadratic form whose value is the number of full twists mod 2 in a neighborhood of ...
Cahit Arf (1910–1997), Turkish mathematician; Science, medicine, and mathematics. Acute renal failure; ... p14arf or ARF tumor suppressor; Other uses. Arf ...
In mathematics, an Arf ring was defined by Lipman (1971) to be a 1-dimensional commutative semi-local Macaulay ring satisfying some extra conditions studied by Cahit Arf . References [ edit ]
In mathematics, Arf semigroups are certain subsets of the non-negative integers closed under addition, that were studied by Cahit Arf . They appeared as the semigroups of values of Arf rings. A subset of the integers forms a monoid if it includes zero, and if every two elements in the subset have a sum that also belongs to the subset. In this ...
İhsan Ketin, geologist; Osman Kibar, engineer and founder of Biosplice; Ioanna Kuçuradi, Professor of Philosophy, President of Turkish Philosophy Association; Behram Kurşunoğlu, physicist
By a theorem of Cahit Arf, any even unimodular lattice has signature divisible by 8, so Rokhlin's theorem forces one extra factor of 2 to divide the signature. A K3 surface is compact, 4 dimensional, and () vanishes, and the signature is −16, so 16 is the best possible number in Rokhlin's theorem.