slides

Instantons in Classical Geometry
Let (M, g) be a compact Riemannian four-manifold.
The Hodge operator ∗ : Ω 2 (M) → Ω 2 (M) obeys ∗ 2 = id and there is an
eigenspace decomposition
Ω 2 (M) = Ω 2 +(M) ⊕ Ω 2 −(M)
into self-dual and anti-self-dual two-forms.
Now fix a smooth SU(2) vector bundle E over M.
We say that a connection ∇ : Γ(E) → Ω 1 (E) is an instanton if its curvature
F = ∇ 2 is a self-dual two-form, i.e. it obeys ∗F = F .
S. Brain (RU) NCG of Self-Dual Gauge Fields Nijmegen, 12th October 2010 3 / 25