  Starting from the entanglement wedge of a multipartite mixed state we
describe a purification procedure which involves the gluing of several copies.
The resulting geometry has non-trivial topology and a single oriented boundary
for each original boundary region. In the purified geometry the original
multipartite entanglement wedge cross section is mapped to a minimal surface of
a particular non-trivial homology class. In contrast each original bipartite
entanglement wedge cross section is mapped to the minimal wormhole throat
around each boundary. Using the bit thread formalism we show how maximal flows
for the bipartite and multipartite entanglement wedge cross section can be
glued together to form maximal multiflows in the purified geometry. The
defining feature differentiating the flows is given by the existence of threads
which cross between different copies of the original entanglement wedge.
Together these demonstrate a possible connection between multipartite
entanglement and the topology of holographic spacetimes.
