Which paper is the "Taubes trick" from?

Question

In symplectic geometry, the "Taubes trick" is an argument used to show that a moduli space $\mathcal{M}(J)$, depending on a parameter $J \in \mathcal{J}$, is cut out transversely for generic choices of $J$. To elaborate, the usual Sard–Smale argument only proves that $\mathcal{M}(J)$ is cut out transversely for generic $J$ in some Banach completion $\mathcal{J}^k$ of the parameter space $\mathcal{J}$. The Taubes trick (roughly) involves choosing a compact exhaustion $\mathcal{M}_1(J) \subseteq \mathcal{M}_2(J) \subseteq \cdots$ of each $\mathcal{M}(J)$ and noting that, by virtue of compactness, each $\mathcal{M}_i(J)$ is cut out transversely for a comeager subset of $\mathcal{J}^k$ which is also open. Since $\mathcal{J}$ is a dense subset of $\mathcal{J}^k$, it follows that $\mathcal{M}_i(J)$ is cut out transversely for an open and dense subset of $\mathcal{J}$, hence $\mathcal{M}(J) = \bigcup_i \mathcal{M}_i(J)$ is cut out transversely for a comeager subset of $\mathcal{J}$.

I have found several sources which attribute this argument to Taubes, e.g., McDuff & Salamon's book on $J$-holomorphic curves and Chris Wendl's various lecture notes. However, none of these sources cite the original paper where this argument is from. Does anyone know where I can find the original source for the "Taubes trick"?

Answer 1

The established reference (see for example arXiv:0912.0651) to Taubes trick is

• C.H. Taubes, Seiberg Witten and Gromov invariants for symplectic 4-manifolds (2000).

This book collects results from four papers by Taubes, including

• C.H. Taubes, Counting pseudo-holomorphic submanifolds in dimension 4, J. Differential Geom. 44, 818–893 (1996).