Deficiency Symmetries of Surgeries in $S^3$

Julian Gibbons

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arXiv · 1304.0367

Deficiency Symmetries of Surgeries in $S^3$

Julian Gibbons

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Abstract

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.

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Julian Gibbons. 2013-04-01. Deficiency Symmetries of Surgeries in $S^3$. https://arxiv.org/abs/1304.0367

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