  Holographic duals for CFTs compactified on a Riemann surface $\Sigma$ with a
twist are cast in the language of wedge holography. $\Sigma$ starts as part of
the field theory geometry in the UV and becomes part of the internal space in
the IR. This allows to associate entanglement entropies with splits of the
internal space in the IR geometry. Decomposing the internal space in the IR and
geometrizing the corresponding subsystems separately leads to two interacting
gravitational systems, similar to the intermediate holographic description in
braneworld models. For $\Sigma=T^2$ the setups are used to model information
transfer from a black hole to a gravitating bath. This leads to Page curves
with a phase structure which precisely mirrors that in braneworld models. The
transition from geometric to non-geometric entropies is also discussed for
$\Sigma=S^2$ as a model for more general internal spaces in AdS/CFT.
