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We demonstrate a way to apply $S^1$-localisation to moduli spaces ofholomorphic curves. We first prove a reinterpretation of Atyiah-Bott$S^1$-localisation, called {\it localisation by pseudocycles} (LbP), for asmooth semifree $S^1$-action on a manifold. We demonstrate that, for certainmoduli spaces of holomorphic curves parametrised by some stratum of thehomotopy quotient of a manifold, we may ``lift" the LbP procedure from theparameter space to the moduli space. As an application we deduce relationsbetween equivariant symplectic classes and Gromov-Witten invariants, thusproving a conjecture of Seidel.

$S^1$-localisation by pseudocycles, lifts to $S^1$-localisation of  moduli spaces, and application to invariants of $S^1$-equivariant symplectic  cohomology