English

The knot complement problem for null-homotopic knots

Geometric Topology 2025-11-10 v1

Abstract

We prove that for three-manifolds satisfying a certain algebraic condition on their fundamental group, null-homotopic knots are determined by their complements. This answers a Kirby Problem posed by Boileau for this special case of 3-manifolds. The argument uses techniques in instanton Floer homology and SU(2)-representation varieties.

Keywords

Cite

@article{arxiv.2511.05472,
  title  = {The knot complement problem for null-homotopic knots},
  author = {Aliakbar Daemi and Tye Lidman},
  journal= {arXiv preprint arXiv:2511.05472},
  year   = {2025}
}

Comments

32 pages, 6 figures

R2 v1 2026-07-01T07:26:36.691Z