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The ℤ/2-equivariant Seiberg--Witten Floer cohomology of the $(2, 1)$-cable is an unknot detector
Abstract
We prove that a knot K ⊂ S3 is the unknot if and only if the ℤ/2-equivariant Seiberg--Witten Floer cohomology of the double cover branched along the $(2, 1)$-cable of K has no 𝔽2[Q]-torsion. The proof combines the Thom--Gysin exact sequence, the Montesinos trick, and the genus bound for L-space surgeries.
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BibTeX
@misc{iida2026ℤ2equivariant,
title = {{The $\mathbbZ/2$-equivariant Seiberg--Witten Floer cohomology of the $(2, 1)$-cable is an unknot detector}},
author = {Nobuo Iida and Tatsumasa Suzuki},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.04823},
eprint = {2611.04823},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.04823},
}
RIS
TY - UNPB
TI - The ℤ/2-equivariant Seiberg--Witten Floer cohomology of the $(2, 1)$-cable is an unknot detector
AU - Nobuo Iida
AU - Tatsumasa Suzuki
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.04823
UR - https://arxiv.org/abs/2611.04823
AB - We prove that a knot K ⊂ S^3 is the unknot if and only if the ℤ/2-equivariant Seiberg--Witten Floer cohomology of the double cover branched along the $(2, 1)$-cable of K has no 𝔽_2[Q]-torsion. The proof combines the Thom--Gysin exact sequence, the Montesinos trick, and the genus bound for L-space surgeries.
ER -