the same holds with the hat version of Heegaard Floer homology.

At the same time, Wehrheim and Woodward developed a general framework, called Floer field theory, for dealing with symplectic constructions similar with Atiyah’s procedure, and provided a general criterion for these to give topological invariants: the assignment $$\begin{aligned}
\Sigma &\mapsto M(\Sigma), \\ H_i &\mapsto L(H_i)\end{aligned}$$ should be functorial in a certain sense, see [@WWfft; @Wehrheimphilo].

The goal of the present paper is to investigate the effect of connected sums and Dehn surgery on symplectic instanton homology. Regarding the second operation, in similar theories, one usually has long exact sequences relating the invariants associated to a “surgery triad” (see Definition \[def:triad\]), for example the $0,1, \infty$ -surgeries along a framed knot: see [@Floertri] for instanton homology, [@OSzholodisk2] for Heegaard Floer theory, and [@KMOSzchir] for monopole homology.

However, the existence of such an exact sequence in instanton homology must face the following problem: three manifolds forming a triad can never be simultaneously integral homology spheres. Floer overcame this issue by using a nontrivial $SO(3)$-bundle over the $S^2\times S^1$-homology manifold appearing in the triad. Even though HSI homology is well-defined for every closed oriented 3-manifold, we will see that the same phenomena 