  Topological structure has been extensively studied and confirmed in highly
correlated condensed matter physics. We explore the gravitational waves emitted
from binary neutron star mergers using the pseudoconformal model for dense
nuclear matter for compact stars. This model considers the topology change and
the possible emergent scale symmetry and satisfies all the constraints from
astrophysics. We find that the location of the topology change affects
gravitational waves dramatically owing to its effect on the equation of state.
In addition, the effect of this location on the waveforms of the gravitational
waves is within the ability of the on-going and up-coming facilities for
detecting gravitational waves, thus suggesting a possible way to measure the
topology structure in nuclear physics.
