Explicit trajectory communication can be used to coordinate multiple robots, but communicating at every planning iteration can lead to congestion of the communication network, increase message delays and message loss. At the same time, collision-free trajectory planning is often formulated as a nonconvex optimization problem, which can converge to different locally optimal solutions across consecutive planning iterations.When this happens, a robots planned motion can switch between distinct high-level avoidance behaviors, such as passing an obstacle on the left versus on the right, which can lead to inefficient or unsafe behavior. Topology-based motion planners address this by explicitly computing multiple candidate motion plans that represent these different passing decisions, each associated with a distinct homotopy class. This work asks how (changes in) homotopy-class representations can trigger communication to reduce communication load while maintaining safe and efficient behavior. Building on the topology-driven trajectory optimization(T-MPC) approach of [ 1], we propose T-DMPC, a topology-aware distributed motion planner in which each robot, computes multiple guidance trajectories in distinct homotopy classes and refines them via parallel local trajectory optimization within the corresponding homotopy classes, selects a solution using a consistent decision rule that prioritizes the previously executed homotopy class, and communicates the selected trajectory using an event-triggered policy. Communication is triggered by homotopy changes and complemented by geometric-deviation and time-based triggers to bound trajectory staleness. In addition, the robots communicate a fallback trajectory during planning failures (e.g. infeasibility). We evaluate T-DMPC on antipodal swap maneuvers with 2 and3 robots in simulation and on physical robots, comparing against T-VMPC (no communication, constant-velocity predictions) and T-AMPC (always communicate). The experiments show that, T-DMPC achieves task duration and traveled distance comparable to T-AMPC and T-VMPC, while reducing communication to about 9.8% (2 robots) and 13.2% (3 robots) of planning iterations in simulation, and 17.8% (2 robots) and 13.2% (3 robots) in real-world experiments, with no observed physical collisions. Ablations however show that topology-change alone is insufficient for safety,motivating the combined trigger design.