• DOI:10.5802/AFST.1479
• Corpus ID: 11403200

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}
}

• Eileen N Li, Yi Ni
• Published 4 October 2013
• Mathematics
• arXiv: Geometric Topology

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 manifold must be one of ten spherical space forms. As knot Floer homology carries a lot of information about the knot, this gives a strong evidence to Boyer--Zhang's conjecture.