In mathematics, the Arf invariant of a nonsingular quadratic form over a field of characteristic 2 was defined by the Turkish mathematician Cahit Arf, who began the systematic study of quadratic forms over arbitrary fields of characteristic 2. The Arf invariant serves, in characteristic 2, the role the discriminant plays for quadratic forms in other characteristics, and Arf used it, among other tools, in his effort to classify quadratic forms in characteristic 2.
Facts
Origin Yeardefined by Turkish mathematician Cahit Arf (1941) Connections
Attributed To
Source Arf Invariant (Wikipedia)
In Branch
Source Arf Invariant (Wikipedia)
Is Kind Of Object
Sources
1. Arf Invariant (Wikipedia)
Lead section
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.
In Branch: Geometric Topology, Lead paragraph
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-dimensional 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.
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