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A note on realizing triples of slice, concordance and Seifert genera
Abstract
We show that every triple of integers (a,b,c) satisfying 1≤ a≤ b≤ c is realized as the smooth slice genus, smooth concordance genus, and Seifert genus of a knot, respectively. This proves a conjecture of Kearney.
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BibTeX
@misc{wang2026note,
title = {{A note on realizing triples of slice, concordance and Seifert genera}},
author = {Boning Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11849},
eprint = {2610.11849},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11849},
}
RIS
TY - UNPB
TI - A note on realizing triples of slice, concordance and Seifert genera
AU - Boning Wang
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.11849
UR - https://arxiv.org/abs/2610.11849
AB - We show that every triple of integers (a,b,c) satisfying 1≤ a≤ b≤ c is realized as the smooth slice genus, smooth concordance genus, and Seifert genus of a knot, respectively. This proves a conjecture of Kearney.
ER -