Half-integral finite surgeries on knots in S

Suppose that a hyperbolic knot in S admits a finite surgery, Boyer and Zhang proved that the surgery slope must be either integral or halfintegral, 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 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.