The chemical and topological structure of polymer networks can seldom be orthogonally controlled. For example, novel network topologies are often accessed via the direct incorporation of supramolecular assemblies into the network structure, introducing potentially undesirable chemical components. Here, we address this deficiency by programming topology into network precursors through the incorporation of self-assembly motifs in leaving groups, which become "traceless topological modifiers." Our method enables us to control polymer network topology using self-assembled structures as templates that are not themselves incorporated into the network. We demonstrate this strategy using a model network formed through potassium acyltrifluoroborate (KAT) ligation. Two four-arm polyethylene glycol (PEG)-based star polymers prepared with either O-ethyl or O-octyl carbamoyl hydroxylamine chain ends serve as network precursors, where differences in chain end hydrophobicity produce different self-assembly states in solution. Addition of a bis-KAT reagent to these star polymers induces amide bond formation and concomitant expulsion of the ethyl or octyl traceless topological modifiers, producing topologically isomeric PEG gels with identical chemical compositions yet vastly different physical properties. This work highlights the impact of topology on polymer network properties and provides a new strategy, traceless topological modification, for polymer network design.