THE SMITH CONJECTURE IN DIMENSION 4 AND EQUIVARIANT GAUGE-THEORY

We study actions of a compact, not necessarily connected Lie group on a compact, oriented, definite 4-manifold. From the equivariant geometry of the one-instanton moduli space, we derive in a geometrical way some properties of the fixed point set of the group action in the 4-manifold, which imply the Smith conjecture.