slides

Instantons on the Euclidean Four-Sphere
For simplicity, we focus on studying instantons on the Euclidean four-sphere S 4 .
Note that SU(2) bundles over S 4 are indexed by their ‘topological charge’
k = ch2(E) ∈ H 4 (S 4 , Z).
Let us write Mk for the moduli space of instantons on an SU(2) vector
bundle E over S 4 with fixed topological charge k ∈ Z.
We’re interested in moduli spaces of instantons on noncommutative
four-spheres....
....so let’s begin by studying the construction of instantons on classical S 4
from the point of view of noncommutative geometry (i.e. in terms of
function algebras, projective modules,...).
S. Brain (RU) NCG of Self-Dual Gauge Fields Nijmegen, 12th October 2010 5 / 25