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arXiv · 2610.10338

Zero-surgery characterises Whitehead doubles

Alice Merz·Diego Santoro
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Abstract

We show that zero is a characterising slope for the untwisted Whitehead double of any knot $K$. More generally, this holds for all $n$-twisted Whitehead doubles of $K$, with the assumption that $n\ne pq$ if $K$ is a non-trivial $(p,q)$-torus knot or $(p,q)$-cable. In particular, zero is a characterising slope for all twist knots.

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Alice Merz, Diego Santoro. 2026-10-07. Zero-surgery characterises Whitehead doubles. https://arxiv.org/abs/2610.10338

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