Misha Schmalian

Lens space surgeries on knots of small genus

We prove that the $(-2,3,7)$ pretzel knot is the only hyperbolic knot of genus at most $5$ with a lens space surgery. Our key technical result asserts that if a genus-$g$ hyperbolic knot $K$ has an elliptic surgery of slope greater than $4g-3$, then the invariant foliations of its monodromy have an orientation that is...