We prove that all rational slopes are characterizing for the knot , except possibly for positive integers. Along the way, we classify the Dehn surgeries on knots in that produce the Brieskorn sphere , and we study knots on which large integral surgeries are almost L‐spaces.
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Free, publicly-accessible full text available January 1, 2025
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Suppose
is an admissible Heegaard diagram for a balanced sutured manifold$\mathcal {H}$ . We prove that the number of generators of the associated sutured Heegaard Floer complex is an upper bound on the dimension of the sutured instanton homology$(M,\gamma )$ . It follows, in particular, that strong L-spaces are instanton L-spaces.$\mathit {SHI}(M,\gamma )$