# Half-integral finite surgeries on knots in $S^3$

@article{Li2013HalfintegralFS, title={Half-integral finite surgeries on knots in \$S^3\$}, author={Eileen N Li and Yi Ni}, journal={arXiv: Geometric Topology}, year={2013} }

Suppose that a hyperbolic knot in $S^3$ admits a finite surgery, Boyer and Zhang proved that the surgery slope must be either integral or half-integral, and they conjectured that the latter case does not happen. Using the correction terms in Heegaard Floer homology, we prove that if a hyperbolic knot in $S^3$ admits a half-integral finite surgery, then the knot must have the same knot Floer homology as one of eight non-hyperbolic knots which are known to admit such surgeries, and the resulting…

## 12 Citations

Integral finite surgeries on knots in S3

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Using the correction terms in Heegaard Floer homology, we prove that if a knot in $S^3$ admits a positive integral $\mathbf{T}$-, $\mathbf{O}$- or $\mathbf{I}$-type surgery, it must have the same…

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We show that on a hyperbolic knot K in S, the distance between any two finite surgery slopes is at most 2 , and consequently, there are at most three nontrivial finite surgeries. Moreover, in the…

Finite Dehn surgeries on knots in $S^3$

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We show that on a hyperbolic knot $K$ in $S^3$, the distance between any two finite surgery slopes is at most two and consequently there are at most three nontrivial finite surgeries. Moreover in…

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Let $K$ be a rationally null-homologous knot in a $3$-manifold $Y$, equipped with a nonzero framing $\lambda$, and let $Y_\lambda(K)$ denote the result of $\lambda$-framed surgery on $Y$. Ozsv\'ath…

Dehn Surgery on Knots in S3 Producing Nil Seifert Fibered Spaces

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We prove that there are exactly 6 Nil Seifert fibred spaces which can be
obtained by Dehn surgeries on non-trefoil knots in S^3, with {60, 144, 156,
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Non-integer characterizing slopes for torus knots

- Mathematics
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A slope $p/q$ is a characterizing slope for a knot $K$ in $S^3$ if the oriented homeomorphism type of $p/q$-surgery on $K$ determines $K$ uniquely. We show that for each torus knot its set of…

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We prove that there are exactly 6 Nil Seifert fibred spaces which can be obtained by Dehn surgeries on non-trefoil knots in S, with {60, 144, 156, 288, 300} as the exact set of all such surgery…

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We provide infinitely many rational homology 3-spheres with weight-one fundamental groups which do not arise from Dehn surgery on knots in $S^3$. In contrast with previously known examples, our…

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This paper explores two questions: (1) Which bigraded groups arise as the knot Floer homology of a knot in the three-sphere? (2) Given a knot, how many distinct knots share its Floer homology?…

The prism manifold realization problem

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We continue our study of the realization problem for prism manifolds. Every prism manifold can be parametrized by a pair of relatively prime integers $p>1$ and $q$. We determine a complete list of…

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