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- Arf_invariant abstract "In mathematics, the Arf invariant of a nonsingular quadratic form over a field of characteristic 2 was defined by Turkish mathematician Cahit Arf (1941) when he started the systematic study of quadratic forms over arbitrary fields of characteristic 2. The Arf invariant is the substitute, in characteristic 2, of the discriminant for quadratic forms in characteristic not 2. Arf used his invariant, among others, in his endeavor to classify quadratic forms in characteristic 2.In the special case of the 2-element field F2 the Arf invariant can be described as the element of F2 that occurs most often among the values of the form. Two nonsingular quadratic forms over F2 are isomorphic if and only if they have the same dimension and the same Arf invariant. This fact was essentially known to Dickson (1901), even for any finite field of characteristic 2, and it follows from Arf's results for an arbitrary perfect field. An assessment of Arf's results in the framework of the theory of quadratic forms can be found in,The Arf invariant is particularly applied in geometric topology, where it is primarily used to define an invariant of (4k + 2)-dimensional manifolds (singly even-dimension manifolds: surfaces (2-manifolds), 6-manifolds, 10-manifolds, etc.) with certain additional structure called a framing, and thus the Arf–Kervaire invariant and the Arf invariant of a knot. The Arf invariant is analogous to the signature of a manifold, which is defined for 4k-dimensional manifolds (doubly even-dimensional); this 4-fold periodicity corresponds to the 4-fold periodicity of L-theory. The Arf invariant can also be defined more generally for certain 2k-dimensional manifolds.".
- Arf_invariant thumbnail 10_Türk_Lirası_reverse.jpg?width=300.
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- Arf_invariant wikiPageWikiLink Arf_invariant_(knot).
- Arf_invariant wikiPageWikiLink Arf_invariant_of_a_knot.
- Arf_invariant wikiPageWikiLink Arf–Kervaire_invariant.
- Arf_invariant wikiPageWikiLink C.T.C._Wall.
- Arf_invariant wikiPageWikiLink C._T._C._Wall.
- Arf_invariant wikiPageWikiLink Category:Quadratic_forms.
- Arf_invariant wikiPageWikiLink Category:Surgery_theory.
- Arf_invariant wikiPageWikiLink Characteristic_(algebra).
- Arf_invariant wikiPageWikiLink Clifford_algebra.
- Arf_invariant wikiPageWikiLink Cobordism.
- Arf_invariant wikiPageWikiLink Compact_space.
- Arf_invariant wikiPageWikiLink Connected_space.
- Arf_invariant wikiPageWikiLink Connected_sum.
- Arf_invariant wikiPageWikiLink De_Rham_invariant.
- Arf_invariant wikiPageWikiLink Discriminant.
- Arf_invariant wikiPageWikiLink Doubly_even.
- Arf_invariant wikiPageWikiLink Embedding.
- Arf_invariant wikiPageWikiLink European_Mathematical_Society.
- Arf_invariant wikiPageWikiLink Exotic_sphere.
- Arf_invariant wikiPageWikiLink Field_(mathematics).
- Arf_invariant wikiPageWikiLink Framed_manifold.
- Arf_invariant wikiPageWikiLink GF(2).
- Arf_invariant wikiPageWikiLink Genus.
- Arf_invariant wikiPageWikiLink Geometric_topology.
- Arf_invariant wikiPageWikiLink Glen_Bredon.
- Arf_invariant wikiPageWikiLink Homotopy_groups_of_spheres.
- Arf_invariant wikiPageWikiLink Immersion_(mathematics).
- Arf_invariant wikiPageWikiLink Intersection_form_(4-manifold).
- Arf_invariant wikiPageWikiLink Intersection_theory.
- Arf_invariant wikiPageWikiLink Isotropic_quadratic_form.
- Arf_invariant wikiPageWikiLink Isotropy_index.
- Arf_invariant wikiPageWikiLink John_Milnor.
- Arf_invariant wikiPageWikiLink Jones_polynomial.
- Arf_invariant wikiPageWikiLink Kervaire.
- Arf_invariant wikiPageWikiLink Kervaire_invariant.
- Arf_invariant wikiPageWikiLink Knot_invariant.
- Arf_invariant wikiPageWikiLink L-theory.
- Arf_invariant wikiPageWikiLink Lev_Pontryagin.
- Arf_invariant wikiPageWikiLink Link_concordance.
- Arf_invariant wikiPageWikiLink Manifold.
- Arf_invariant wikiPageWikiLink Mathematician.
- Arf_invariant wikiPageWikiLink Mathematics.
- Arf_invariant wikiPageWikiLink Michel_Kervaire.
- Arf_invariant wikiPageWikiLink Milnor.
- Arf_invariant wikiPageWikiLink Orientability.
- Arf_invariant wikiPageWikiLink Oriented.
- Arf_invariant wikiPageWikiLink Parallelizable.
- Arf_invariant wikiPageWikiLink Parallelizable_manifold.
- Arf_invariant wikiPageWikiLink Pontrjagin-Thom_construction.
- Arf_invariant wikiPageWikiLink Quadratic_form.
- Arf_invariant wikiPageWikiLink Quadratic_refinement.
- Arf_invariant wikiPageWikiLink Seifert_surface.
- Arf_invariant wikiPageWikiLink Signature_(topology).
- Arf_invariant wikiPageWikiLink Signature_of_a_manifold.
- Arf_invariant wikiPageWikiLink Singly_and_doubly_even.
- Arf_invariant wikiPageWikiLink Singly_even.
- Arf_invariant wikiPageWikiLink Slice_knot.
- Arf_invariant wikiPageWikiLink Spin_structure.
- Arf_invariant wikiPageWikiLink Springer-Verlag.
- Arf_invariant wikiPageWikiLink Springer_Science+Business_Media.
- Arf_invariant wikiPageWikiLink Steenrod_algebra.
- Arf_invariant wikiPageWikiLink Steenrod_square.
- Arf_invariant wikiPageWikiLink Surface.
- Arf_invariant wikiPageWikiLink Surgery_theory.
- Arf_invariant wikiPageWikiLink Symplectic_vector_space.
- Arf_invariant wikiPageWikiLink Thom_space.
- Arf_invariant wikiPageWikiLink Torus.
- Arf_invariant wikiPageWikiLink Totally_isotropic.
- Arf_invariant wikiPageWikiLink Turkic_peoples.
- Arf_invariant wikiPageWikiLink Vector_bundle.
- Arf_invariant wikiPageWikiLink W._B._R._Lickorish.
- Arf_invariant wikiPageWikiLink W._B._Raymond_Lickorish.
- Arf_invariant wikiPageWikiLink Whitney_embedding_theorem.
- Arf_invariant wikiPageWikiLink William_Browder_(mathematician).
- Arf_invariant wikiPageWikiLink Ε-quadratic_form.
- Arf_invariant wikiPageWikiLink File:10_Türk_Lirası_reverse.jpg.
- Arf_invariant wikiPageWikiLinkText "Arf invariant".
- Arf_invariant author "A.V. Chernavskii".
- Arf_invariant authorlink "Cahit Arf".
- Arf_invariant first "Cahit".
- Arf_invariant hasPhotoCollection Arf_invariant.
- Arf_invariant id "A/a013230".
- Arf_invariant last "Arf".
- Arf_invariant title "Arf invariant".
- Arf_invariant wikiPageUsesTemplate Template:Citation.
- Arf_invariant wikiPageUsesTemplate Template:Harvs.
- Arf_invariant wikiPageUsesTemplate Template:Harvtxt.
- Arf_invariant wikiPageUsesTemplate Template:Reflist.
- Arf_invariant wikiPageUsesTemplate Template:Springer.
- Arf_invariant year "1941".
- Arf_invariant subject Category:Quadratic_forms.
- Arf_invariant subject Category:Surgery_theory.
- Arf_invariant comment "In mathematics, the Arf invariant of a nonsingular quadratic form over a field of characteristic 2 was defined by Turkish mathematician Cahit Arf (1941) when he started the systematic study of quadratic forms over arbitrary fields of characteristic 2. The Arf invariant is the substitute, in characteristic 2, of the discriminant for quadratic forms in characteristic not 2.".
- Arf_invariant label "Arf invariant".