  We explore the main physical processes which potentially affect the
topological signal in the Cosmic Microwave Background (CMB) for a range of
toroidal universes. We consider specifically reionisation, the integrated
Sachs-Wolfe (ISW) effect, the size of the causal horizon, topological defects
and primordial gravitational waves. We use three estimators: the information
content, the S/N statistic and the Bayesian evidence. While reionisation has
nearly no effect on the estimators, we show that taking into account the ISW
strongly decreases our ability to detect the topological signal. We also study
the impact of varying the relevant cosmological parameters within the 2 sigma
ranges allowed by present data. We find that only Omega_Lambda, which
influences both ISW and the size of the causal horizon, significantly alters
the detection for all three estimators considered here.
