  We study real time correlators in strongly coupled N=4 supersymmetric
Yang-Mills theory on dS_3 x S^1, with antiperiodic boundary conditions for
fermions on the circle. When the circle radius is larger than a critical value,
the dual geometry is the so-called "topological AdS_5 black hole". Applying the
Son- Starinets recipe in this background we compute retarded glueball
propagators which exhibit an infinite set of poles yielding the quasinormal
frequencies of the topological black hole. The imaginary parts of the
propagators exhibit thermal effects associated with the Gibbons-Hawking
temperature due to the cosmological horizon of the de Sitter boundary. We also
obtain R-current correlators and find that after accounting for a small
subtlety, the Son-Starinets prescription yields the retarded Green's functions.
The correlators do not display diffusive behaviour at late times. Below the
critical value of the circle radius, the topological black hole decays to the
AdS_5 "bubble of nothing". Using a high frequency WKB approximation, we show
that glueball correlators in this phase exhibit poles on the real axis. The
tunnelling from the black hole to the bubble is interpreted as a hadronization
transition.
