All principal congruence link groups
Mark D. Baker, Matthias Goerner, Alan W. Reid

TL;DR
This paper systematically enumerates all principal congruence link complements in the 3-sphere, addressing a longstanding question posed by Thurston and expanding the understanding of these special hyperbolic 3-manifolds.
Contribution
It provides a complete classification of principal congruence link groups in $S^3$, filling a gap in the topology of hyperbolic 3-manifolds.
Findings
All principal congruence link complements in $S^3$ are enumerated.
The classification confirms the finiteness of such link groups.
Answers a question posed by Thurston regarding these link complements.
Abstract
We enumerate all the principal congruence link complements in , there by answering a question of W. Thurston. Related articles: "Technical Report: All Principal Congruence Link Groups" (arXiv:1902.04722), "All Known Principal Congruence Links" (arXiv:1902.04426).
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