  We investigate the multipartite entanglement of a uniformly curved quantum 3D
space region with boundary, realised in terms of spin networks defined on a
graph with non trivial SU(2) holonomies, in the framework of loop quantum
gravity. The presence of intrinsic curvature in the region is encoded in
closure (topological) defects associated with tag-spins attached to the
vertices of the graph. For such states, we generalise the bulk-to-boundary
mapping as to include the space of tags in an extended boundary space: bulk
information is shared among generically entangled boundary surfaces and
intrinsic curvature degrees of freedom. We model the quantum region on a
tripartite system composed by two (complementary) boundary subregions and the
set of bulk tags. Via replica techniques, we can compute the typical value of
the logarithmic negativity of the reduced boundary, described as an open
quantum system, in a large spin regime. We find three entanglement regimes,
depending on the ratio between the number of tags (curvature) and the area of
the dual surface at the boundary. These are well described by the generalised
Page curve of a tripartite random state. In particular, we find area scaling
behaviour for negativity in case of small curvature, while for large curvature
the negativity vanishes, suggesting an effective thermalization of the
boundary. Remarkably, the PPT character of the mixed boundary state corresponds
to a change in the effective topology of the network, with the two boundary
subregions becoming disconnected.
