Characterizing slopes for $5_2$

Abstract

We prove that all rational slopes are characterizing for the knot $5_2$, except possibly for positive integers. Along the way, we classify the Dehn surgeries on knots in $S^3$ that produce the Brieskorn sphere $\Sigma (2,3,11)$, and we study knots on which large integral surgeries are almost L-spaces.

arXiv comment54 pages, 5 figures; v2: accepted version

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Cited by in corpus (4)

• Characterising slopes for hyperbolic knots and Whitehead doubles
• Floer homology and non-fibered knot detection
• Knot surgery formulae for instanton Floer homology I: the main theorem
• Framed instanton homology and concordance, II