Every non-trivial knot group is fully residually perfect
Abstract
Abstract Given a class script upper P P $\mathcal{P}$ of groups we say that a group G is fully residually script upper P P $\mathcal{P}$ if for any finite subset F of G , there exists an epimorphism from G to a group in script upper P P $\mathcal{P}$ which is injective on F . It is known that any non-trivial knot group is fully residually finite, but not residually free. For hyperbolic knots, its knot group is fully residually closed hyperbolic 3–manifold group, and such a group is fully residually simple. In this paper, we show that every non-trivial knot group is fully residually perfect, closed 3–manifold group.
Fields of Study & Subjects
Geometric and Algebraic Topology
Advanced Numerical Analysis Techniques
Publication details
- Journal / source
- Mathematical Proceedings of the Cambridge Philosophical Society
- Publisher
- Cambridge University Press (CUP)
- Pages
- 1–21
- Publication date
- 7 August 2026
- Language
- EN