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We examine certain symmetries in the deficiencies of a rational surgery on a knot in   $S^3$   by comparing the   ${\rm Spin}^c$  -structures on the rational surgery with those on a related integral surgery. We then provide an application of these symmetries in the form of a theorem that obstructs Dehn surgeries in   $S^3$  . This last part unifies and generalizes two theorems by Greene which underlie his work on the cabling conjecture, the lens space realization problem, and the unknotting number of alternating 3-braids.

Deficiency Symmetries of Surgeries in S 3