Lens surgeries along the $n$-twisted Whitehead link

TL;DR

This paper classifies lens surgeries along the n-twisted Whitehead link, providing conditions based on Alexander polynomials and exploring their applications in knot theory.

Contribution

It establishes necessary conditions for lens surgeries on the n-twisted Whitehead link using Alexander polynomial analysis, including specific surgery coefficients.

Findings

Lens surgeries only occur when n=1 or with specific surgery coefficients.

Alexander polynomial provides useful necessary conditions for lens surgeries.

Results extend understanding of Dehn surgeries yielding lens spaces.

Abstract

We determine lens surgeries (i.e.\ Dehn surgery yielding a lens space) along the $n$-twisted Whitehead link. To do so, we first give necessary conditions to yield a lens space from the Alexander polynomial of the link as: (1) $n=1$ (i.e. the Whitehead link), and (2) one of surgery coefficients is 1, 2 or 3. Our interests are not only lens surgery itself but also how to apply the Alexander polynomial for this kind of problems.