  The topological calculation of Aharonov-Bohm phases associated with D-branes
in the absence of a Neveu-Schwarz B-field is explored. The K-theoretic
classification of Ramond-Ramond fields in Type II and Type I theories is used
to produce formulae for the Aharonov-Bohm phase associated with a torsion flux.
A topological construction shows that K-theoretic pairings to calculate such
phases exist and are well-defined. An analytic perspective is then taken,
obtaining a means for determining Aharonov-Bohm phases by way of the reduced
eta-invariant. This perspective is used to calculate the phase for an
experiment involving the $(-1)-8$ system in Type I theory, and compared with
previous calculations performed using different methods.
