English

(1,1) almost L-space knots

Geometric Topology 2025-10-15 v2

Abstract

We give a diagrammatic characterization of the (1,1)(1,1) knots in the three-sphere and lens spaces which admit large Dehn surgeries to manifolds with Heegaard Floer homology of next-to-minimal rank. This is inspired by a corresponding result for (1,1)(1,1) knots which admit large Dehn surgeries to manifolds with Heegaard Floer homology of minimal rank due to Greene-Lewallen-Vafaee.

Keywords

Cite

@article{arxiv.2304.11475,
  title  = {(1,1) almost L-space knots},
  author = {Fraser Binns and Hugo Zhou},
  journal= {arXiv preprint arXiv:2304.11475},
  year   = {2025}
}

Comments

22 pages, 14 figures. Revisions throughout following the suggestions from the referee. This is the version to appear in the Indiana University Mathematics Journal

R2 v1 2026-06-28T10:14:38.627Z