A polynomial invariant for links in lens spaces

TL;DR

This paper introduces a new polynomial invariant for links in lens spaces that satisfies the HOMFLY skein relation, supported by a skein theory of toroidal grid diagrams in such spaces.

Contribution

It develops the first polynomial invariant for links in lens spaces and establishes a skein theory based on toroidal grid diagrams.

Findings

Existence of a polynomial invariant satisfying HOMFLY skein relation in lens spaces

Development of skein theory for toroidal grid diagrams in lens spaces

Foundation for further link invariants in 3-manifolds

Abstract

We prove the existence of a polynomial invariant that satisfies the HOMFLY skein relation for links in a lens space. In the process we also develop a skein theory of toroidal grid diagrams in a lens space.