U torsion structure in Heegaard Floer homology

@misc{chen2026torsion,
  title = {{U torsion structure in Heegaard Floer homology}},
  author = {Yuhui Chen and Shunyu Wan},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.27646},
  eprint = {2610.27646},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.27646},
}

TY  - UNPB
TI  - U torsion structure in Heegaard Floer homology
AU  - Yuhui Chen
AU  - Shunyu Wan
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2610.27646
UR  - https://arxiv.org/abs/2610.27646
AB  - We construct infinite families of Brieskorn spheres with three singular fibers for which the difference between the largest and the second largest length of U-torsion in their Heegaard Floer homology HF^- increases to infinity as the family parameter increases. In particular, these families give a negative answer to the strong geography restriction problem by Alfieri and Binns \cite[Question 1.10]{AB24} which was added to the recent K3 list \cite[Problem 3.55, Remark(5)]{K3}. As a consequence of the results by Alfieri and Binns, these families give the examples of integer homology spheres that are neither surgery on a knot nor large surgery on links.
ER  -