  Over the last three decades entanglement entropy has been obtained for
quantum fields propagating in genus zero topologies (Spheres). For scalar
fields propagating in these topologies, it has been shown that the entanglement
entropy scales as area. In the last few years non-trivial topologies are
increasingly relevant for different areas. For instance, in describing quantum
phases, it has been realized that long-range entangled states are described by
topological order. If quantum entanglement can plausibly provide explanation
for these, it then imperative to obtain entanglement entropy in these
topologies. In this work, using two different methods, we explicitly show that
the entanglement entropy scales as area of the genus-1 geometry.
