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Motivation<br />
What is the difference between a classical four-manifold and a<br />
noncommutative four-manifold?<br />
To find out, we’d like to ‘probe’ their geometric structures somehow.<br />
Donaldson did this for a classical four-manifold M by looking at the moduli<br />
space of self-dual gauge fields (instantons) on M. Can we do the same for a<br />
noncommutative manifold?<br />
In this talk, we ask:<br />
◮ how do we construct instantons on a noncommutative manifold?<br />
◮ can we use them to ‘detect’ something about the noncommutative differential<br />
structure?<br />
S. Brain (RU) NCG of Self-Dual Gauge Fields Nijmegen, 12th October 2010 2 / 25