The Witten-Reshetikhin-Turaev invariant of a knot in a lens space

TL;DR

This paper computes the Witten-Reshetikhin-Turaev invariant for knots in lens spaces of type L(m,1) at roots of unity and analyzes its asymptotic behavior as the root order N becomes large.

Contribution

It provides explicit calculations of the invariant for knots in lens spaces and explores its asymptotic properties for large N, extending previous work on quantum invariants.

Findings

Explicit formula for the invariant in lens spaces

Asymptotic analysis of the invariant as N grows large

Insights into quantum invariants in 3-manifold topology

Abstract

We calculate the Witte-Reshetikhi-Turaev invariant for a knot in the lens space of type L(m,1) for the N-th root of unity, and study its asymptotic behavior for large N.