Models of the mechanical response of glassy polymers commonly assume that entanglements inherited from the melt act like chemical cross-links. The predictions from these network models and the physical picture they are based on are tested by following the evolution of topological constraints in simulations of model polymer glasses. The same behavior is observed for polymers with entanglement lengths Ne that vary by a factor of 3. A prediction for the craze extension ratio A based have the taut configurations it assumes. There is also no on the network model describes trends with Ne, but polymers do evidence of the predicted geometrically necessary entanglement loss. While the number of entanglements remains constant, the identity of the chains forming constraints changes. The same relation between the amount of entanglement exchange and nonaffine displacement of monomers is found for crazing and thermal diffusion in end-constrained melts. In both cases, about 1/3 of the constraints change when monomers move by the tube radius. The results show that chains in deformed glassy polymers are constrained by their rheological tubes rather than by entanglements that act like discrete cross-links.