The Pin(2)-monopole equations are a variant of the Seiberg-Witten
equations which can be considered as a real version of the SW
equations.
A Pin(2)-monopole version of the Seiberg-Witten invariants is defined,
and has a special feature that the Pin(2)-monopole invariant can be
nontrivial even when all of the Donaldson and Seiberg-Witten
invariants vanish.
As an application, we construct a new series of exotic 4-manifolds.
We will also talk about the stable cohomotopy Pin(2)-monopole invariant.