PreprintCC BY 4.0arXiv
Zero-surgery characterises Whitehead doubles
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≠ 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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BibTeX
@misc{merz2026zerosurgery,
title = {{Zero-surgery characterises Whitehead doubles}},
author = {Alice Merz and Diego Santoro},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10338},
eprint = {2610.10338},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10338},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Zero-surgery characterises Whitehead doubles
AU - Alice Merz
AU - Diego Santoro
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.10338
UR - https://arxiv.org/abs/2610.10338
AB - 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≠ 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.
ER -