  The coupling between the spin and momentum degrees of freedom due to
spin-orbit interactions (SOI) suggests that the strength of the latter can be
modified by controlling the motion of the charge carriers. In this paper, we
investigate how the effective SOI can be modulated by constraining the motion
of charge carriers to curved waveguides thereby introducing real-space
geometric curvature in their motion. The change in the SOI can in turn induce
topological phase transitions in the system. Specifically, we study how the
introduction of periodic sinusoidal curvature in nanowires with intrinsic SOC
can induce the onset of mid-gap topologically protected edge states, which can
be characterized by a topological invariant or Chern number. The Chern number
corresponds to the number of discrete charges that would be pumped across the
length of the nanowire when the phase of a sliding gate potential relative to
that of the sinusoidal curvature is varied adiabatically over a complete
period. In addition, coupling to an external magnetization can be utilized as
an experimental knob to modify the Chern number by changing the ordering of the
nanowire energy bands. The magnetization can be tuned to achieve large discrete
jumps in the number of pump charges per phase period.
