The G-property of knots

Abstract

A Knot \({K\subset S^{3}}\) is said to satisfy the G-property if for every \({r \in \mathbb{Q}}\) the manifold M(K, r) obtained by rational surgery on K with surgery coefficient r is the boundary of a Stein domain. The problem of finding which knots satisfy the G-property is still wide open. This paper introduces this problem and presents some techniques used to prove that certain infinite families of knots satisfy the G-property.