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.