On the set of L-space surgeries for links

TL;DR

This paper investigates the conditions under which the set of L-space surgeries on links is bounded from below, providing characterizations for algebraic two-component links and extending some results to non-algebraic links.

Contribution

It offers three complete characterizations of boundedness for algebraic two-component links using the $h$-function, Alexander polynomial, and resolution graph.

Findings

Set of L-space surgeries is bounded from below for most algebraic links.

Characterizations are complete for algebraic two-component links.

The $h$-function property extends to non-algebraic L-space links.

Abstract

It it known that the set of L-space surgeries on a nontrivial L-space knot is always bounded from below. However, already for two-component torus links the set of L-space surgeries might be unbounded from below. For algebraic two-component links we provide three complete characterizations for the boundedness from below: one in terms of the $h$-function, one in terms of the Alexander polynomial, and one in terms of the embedded resolution graph. They show that the set of L-space surgeries is bounded from below for most algebraic links. In fact, the used property of the $h$-function is a sufficient condition for non-algebraic L-space links as well.