S}}_a$ is disconnected. However, by an arbitrarily small perturbation of the cohomology class $a$ the two known distinct connected components of ${{\mathcal S}}_a$ merge to a single connected component. McDuff’s paper [@MCDUFF3] also contains a variant of this construction in dimension eight. Consider the manifold $
M := {{\mathbb T}}^2\times S^2\times S^2.
$ Identify the $2$-torus with the product of two circles. For $\theta\in S^1$ and $z\in S^2$ let ${{\varphi}}_{z,\theta}:S^2\to S^2$ be the rotation about the axis through $z$ by the angle $\theta$. Consider the diffeomorphism $\psi:M\to M$ defined by $$\psi(\theta_1,\theta_2,z_1,z_2) 
:= (\theta_1,\theta_2,z_1,{{\varphi}}_{z_1,\theta_1}(z_2)),\qquad
\theta_1,\theta_2\in S^1,\qquad z_1,z_2\in S^2.$$ It acts as the identity on cohomology. Let ${{\omega}}\in{{\Omega}}^2(M)$ be the product symplectic form, where both $S^2$ factors have the same area, and denote $$a:=[{{\omega}}]=[\psi^*{{\omega}}]\in H^2(M;{{\mathbb R}}).$$ McDuff’s theorem asserts that ${{\omega}}$ and $\psi^*{{\omega}}$ can be joined by a path of symplectic forms, but not by a path of cohomologous symplectic forms. The proof that ${{\omega}}$ and $\psi^*{{\omega}}$ are not isotopic cannot be based on the Gromov–Witten invariants because these are invariant under deformation of symplectic forms (equivalence relation (B) in \[para:equiv\]). McDuff’s proof does involve the moduli space of holomorphic spheres. The relevant evaluation maps represent the same homology class but are 