%0 Journal Article
%T Deficiency Symmetries of Surgeries in $S^3$
%A Julian Gibbons
%J Mathematics
%D 2013
%I arXiv
%X We examine certain symmetries in the deficiencies of a rational surgery on a knot in $S^3$ by comparing the $\text{Spin}^c$-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 generalises theorems by Greene underlying his work on the cabling conjecture, the lens space realisation problem, and the unknotting number of alternating 3-braids.
%U http://arxiv.org/abs/1304.0367v1