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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

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