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