It is shown that the well-known wave behaviors of material particles and photons, as well as the newly discovered wave-like structures in the cosmic redshift, are related phenomena that follow conclusively when senders and receivers of photons or material particles are topologically located in manifolds with a dimension difference of one. In this context, the inertial mass of the proton and the electron, their spin properties and the cause of time are derived from basic topological and physical laws. In addition, the quantum geometric basis of relativistic time dilation, the basis of the relativistic energy-momentum relationship and the relationship between energy and time are shown. Finally, it is shown that a curved cosmic space causes a distance-dependent reddening of light and the associated apparent escape velocity of distant cosmic objects, and that this also leads to a topologically conditioned wave structure of this redshift.
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