Algebraic links in lens spaces

Abstract

The lens space [Formula: see text] is the orbit space of a [Formula: see text]-action on the 3-sphere. We investigate polynomials of two complex variables that are invariant under this action, and thus define links in [Formula: see text]. We study properties of these links, and their relationship with the classical algebraic links. We prove that all algebraic links in lens spaces are fibered, and obtain results about their Seifert genus. We find some examples of algebraic knots in [Formula: see text], whose lift in the [Formula: see text]-sphere is a torus link.