Exotic involutions on symplectic 4-manifolds and \(G\)-monopole invariants (Q5930040)

This paper presents the result that no antiholomorphic involution on a closed symplectic manifold is smoothly conjugate to a holomorphic involution. The result assumes the mild condition that the dimensions of the space of invariant self-dual forms is larger than \(1\). This paper relies strongly on the paper [\textit{Y. Ruan}, in ``Topics in symplectic 4-manifolds'', First Int. Press Lect. Ser. 1, 101-116 (1998; Zbl 0939.57024)] where equivalent Seiberg-Witten invariants are defined and used to prove a similar result in the Kähler case. M. Ishida uses his result to construct pairs of irreducible homeomorphic but not diffeomorphic 4-manifolds.