Nullhomotopic knots are determined by their complements

Abstract

We prove that nullhomotopic knots in three-manifolds are determined by their complements. This answers a Kirby Problem posed by Boileau. The argument uses techniques in instanton Floer homology and $SU(2)$-representation varieties.

35 pages, 7 figures. The SU(2)-non-degeneracy assumption is removed. New author list; see Statement of AI use in the introduction