On L-space knots obtained from unknotting arcs in alternating diagrams

Abstract

Let $D$ be a diagram of an alternating knot with unknotting number one. The branched double cover of $S^3$ branched over $D$ is an L-space obtained by half integral surgery on a knot $K_D$. We denote the set of all such knots $K_D$ by $\mathcal{D}$. We characterize when $K_D\in \mathcal{D}$ is a torus knot, a satellite knot or a hyperbolic knot. In a different direction, we show that for a given $n>0$, there are only finitely many L-space knots in $\mathcal{D}$ with genus less than $n$.

22 pages, 20 figures. Uploaded to match version published in New York J. Math. Substantially extended exposition

References in corpus (4)

• Some knots with surgeries yielding lens spaces
• Satellite knots and L-space surgeries
• Twist families of L-space knots, their genera, and Seifert surgeries
• Bounds on alternating surgery slopes