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In arXiv:1611.09927, we constructed a well-defined Lagrangian Floer invariantfor any closed, oriented $3$-manifold $Y$ via the symplectic geometry ofso-called traceless $\mathrm{SU}(2)$-character varieties. This invariant,$\mathrm{SI}(Y)$, which we refer to as the symplectic instanton homology of$Y$, was also shown to satisfy an exact triangle for Dehn surgeries on knotswhich is typical of Floer-theoretic invariants of $3$-manifolds.  In this article, we demonstrate further structural properties of thissymplectic instanton homology. For example, Floer theories are expected toroughly satisfy the axioms of a topological quantum field theory (TQFT), sothat in particular they should be functorial with respect to cobordisms.Following a strategy used by Ozsv\'ath and Szab\'o in the context of HeegaardFloer homology, we prove that our theory is functorial with respect toconnected $4$-dimensional cobordisms, so that cobordisms induce homomorphismsbetween symplectic instanton homologies. We also generalize the surgery exacttriangle by proving that Dehn surgeries on a link $L$ in a $3$-manifold $Y$induce a spectral sequence of symplectic instanton homologies -- the $E^2$-pageis isomorphic to a direct sum of symplectic instanton homologies of allpossible combinations of $0$- and $1$-surgeries on the components of $L$, andthe spectral sequence converges to $\mathrm{SI}(Y)$. For the branched doublecover $\Sigma(L)$ of a link $L \subset S^3$, we show there is a link surgeryspectral sequence whose $E^2$-page is isomorphic to the reduced Khovanovhomology of $L$ and which converges to the symplectic instanton homology of$\Sigma(L)$.

Traceless Character Varieties, the Link Surgeries Spectral Sequence, and Khovanov Homology