  I use the universal instanton formalism to discuss quantum effects in the
open-closed topological string theory of a Calabi-Yau A-model, in the presence
of a multiply-wrapped `Floer' D-brane. This gives a precise meaning (up to the
issue of compactifying the relevant moduli spaces) to the instanton corrections
which affect sigma model and topological string amplitudes. The cohomological
formalism I use recovers the homological approach used by Fukaya and
collaborators in the singly-wrapped case, even though it is not a naive
generalization of the latter. I also prove some non-renormalization theorems
for amplitudes with low number of insertions. The non-renormalization argument
is purely geometric and based on the universal instanton formulation, and thus
it does not assume that the background satisfies the string equations of
motion. These results are valid even though the D-brane background typically
receives worldsheet instanton corrections. I also point out that the localized
form of the boundary BRST operator receives instanton corrections and make a
few comments on the consequences of this effect.
