<p>Displacement speed and flame stretch are analysed in the vicinity of critical points defining local topology using a direct numerical simulation dataset of a turbulent premixed flame. The analysis categorises local topology types as; reactant pocket, tunnel closure, tunnel formation, and product pocket. The influence of local topology on global flame propagation is discussed. Cylindrical topologies are shown to contribute both positively and negatively towards flame stretch while spherical topologies mainly cause local destruction of flame area. The rate of stretch is shown to follow the curvature profile for all topologies. On the other hand, displacement speed is seen to scale the influence of curvature, while together the two determine whether area is produced or destroyed. The role of local diffusion in displacement speed and the role of curvature in defining the stretch rate profile emerge as the main actors for the local change in area. These local changes are shown to impact the global surface area and consequently the global propagation of the flame.</p>