Domain wall (DW) based logic and memory devices require precise control and manipulation of DW in nanowire conduits. The topological defects of Transverse DWs (TDW) are of paramount importance as regards to the deterministic pinning and movement of DW within complex networks of conduits. In-situ control of the DW topological defects in nanowire conduits may pave the way for novel DW logic applications. In this work, we present a geometrical modulation along a nanowire conduit, which allows for the topological rectification/inversion of TDW in nanowires. This is achieved by exploiting the controlled relaxation of the TDW within an angled rectangle. Direct evidence of the logical operation is obtained via magnetic force microscopy measurement.