Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Chen, Yuhui, Wan, Shunyu
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223115711