Revisiting the Arf invariant

The Arf invariant is an invariant of non-singular quadratic forms over Z/2. Although seemingly too simple, it appears in several contexts in geometric topology (as a concordance invariant of knots, in the Freedman-Kirby generalization of Rokhlin theorem, as Kervaire invariant). In the first part of the talk I will introduce Arf invariants and spin structures. I will then show how in low dimensions they relate and make explicit the 4-dimensional nature of the Arf invariant for knots.